Solutions of chapter 19. Indefinite Integrals | RD Sharma - Mathematics (Volume 1) - Class 12

RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 19. Indefinite Integrals

Subject: Maths - Class 12^th

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Chapter Exercises

Exercise 19.2

Exercise 19.3

Exercise 19.4

Exercise 19.5

Exercise 19.6

Exercise 19.7

Exercise 19.8

Exercise 19.9

Exercise 19.10

Exercise 19.11

Exercise 19.12

Exercise 19.13

Exercise 19.14

Exercise 19.15

Exercise 19.16

Exercise 19.17

Exercise 19.18

Exercise 19.19

Exercise 19.20

Exercise 19.21

Exercise 19.22

Exercise 19.23

Exercise 19.24

Exercise 19.25

Exercise 19.26

Exercise 19.27

Exercise 19.28

Exercise 19.29

Exercise 19.30

Exercise 19.31

Exercise 19.32

Very short answer

MCQ

Revision exercise

Exercise 19.2

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

∫ (2 – 3x)(3 + 2x)(1 – 2x)dx

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

∫ (x^e + e^x + e^e) dx

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

14

Evaluate the following integrals:

15

Evaluate the following integrals:

∫√x(3 – 5x) dx

16

Evaluate the following integrals:

17

Evaluate the following integrals:

18

Evaluate the following integrals:

∫ (3x + 4)² dx

19

Evaluate the following integrals:

20

Evaluate the following integrals:

21

Evaluate the following integrals:

22

Evaluate the following integrals:

∫ (se²x + cosec²x) dx

23

Evaluate the following integrals:

24

Evaluate the following integrals:

25

Evaluate the following integrals:

∫ (tan x + cot x)² dx

26

Evaluate the following integrals:

27

Evaluate the following integrals:

28

Evaluate the following integrals:

29

Evaluate the following integrals:

30

Evaluate the following integrals:

31

Evaluate the following integrals:

32

Evaluate the following integrals:

33

Evaluate the following integrals:

34

Evaluate the following integrals:

35

Evaluate the following integrals:

36

Evaluate the following integrals:

37

Evaluate the following integrals:

38

Evaluate the following integrals:

39

Evaluate the following integrals:

40

Evaluate the following integrals:

41

Evaluate the following integrals:

42

Evaluate the following integrals:

43

Evaluate the following integrals:

44

Evaluate the following integrals:

45

If and, find f(x).

46

If f’(x) = x + b, f(1) = 5, f(2) = 13, find f(x).

47

If f’(x) = 8x³ – 2x, f(2) = 8, find f(x).

48

If f’(x) = a sin x + b cos x and f’(0) = 4, f(0) = 3, , find f(x).

49

Write the primitive or anti-derivative of.

Exercise 19.3

1

2

3

4

5

6

7

8

9

10

11

12

13

14

∫ (e^x + 1)² e^x dx

15

16

17

18

∫ tan²(2x – 3)dx

19

Exercise 19.4

1

2

3

4

5

6

Exercise 19.5

1

2

3

4

5

6

7

8

9

10

Exercise 19.6

1

∫ sin²(2x + 5) dx

2

∫ sin³(2x + 1) dx

3

∫ cos⁴ 2x dx

4

∫ sin² b x dx

5

6

7

∫ cos²nx dx

8

Exercise 19.7

1

∫ sin 4x cos 7x dx

2

∫ cos 3x cos 4x dx

3

∫ cos mx cos nx dx, m ≠ n

4

∫ sin mx cos nx dx, m ≠ n

5

∫ sin 2x sin 4x sin 6x dx

6

∫ sin x cos 2x sin 3x dx

Exercise 19.8

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

14

Evaluate the following integrals:

15

Evaluate the following integrals:

16

Evaluate the following integrals:

17

Evaluate the following integrals:

18

Evaluate the following integrals:

19

Evaluate the following integrals:

20

Evaluate the following integrals:

21

Evaluate the following integrals:

22

Evaluate the following integrals:

23

Evaluate the following integrals:

24

Evaluate the following integrals:

25

Evaluate the following integrals:

26

Evaluate the following integrals:

27

Evaluate the following integrals:

28

Evaluate the following integrals:

29

Evaluate the following integrals:

30

Evaluate the following integrals:

31

Evaluate the following integrals:

32

Evaluate the following integrals:

33

Evaluate the following integrals:

34

Evaluate the following integrals:

35

Evaluate the following integrals:

36

Evaluate the following integrals:

37

Evaluate the following integrals:

38

Evaluate the following integrals:

39

Evaluate the following integrals:

40

Evaluate the following integrals:

41

Evaluate the following integrals:

42

Evaluate the following integrals:

43

Evaluate the following integrals:

44

Evaluate the following integrals:

45

Evaluate the following integrals:

46

Evaluate the following integrals:

∫ tan 2x tan 3x tan 5x dx

47

Evaluate the following integrals:

∫ {1 + tan x tan (x + θ)} dx

48

Evaluate the following integrals:

49

Evaluate the following integrals:

50

Evaluate the following integrals:

51

Evaluate the following integrals:

Exercise 19.9

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

∫ cot³x cosec²x dx

8

Evaluate the following integrals:

9

Evaluate the following integrals:

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

14

Evaluate the following integrals:

15

Evaluate the following integrals:

16

Evaluate the following integrals:

17

Evaluate the following integrals:

18

Evaluate the following integrals:

∫ sin⁵ x cos x dx

19

Evaluate the following integrals:

∫ tan^3/2 x sec² x dx

20

Evaluate the following integrals:

21

Evaluate the following integrals:

22

Evaluate the following integrals:

23

Evaluate the following integrals:

24

Evaluate the following integrals:

25

Evaluate the following integrals:

26

Evaluate the following integrals:

27

Evaluate the following integrals:

28

Evaluate the following integrals:

29

Evaluate the following integrals:

30

Evaluate the following integrals:

∫ cotx log sin x dx

31

Evaluate the following integrals:

∫ sec x log (sec x + tan x) dx

32

Evaluate the following integrals:

∫ cosec x log (cosec x – cot x) dx

33

Evaluate the following integrals:

∫ x³ cos x⁴ dx

34

Evaluate the following integrals:

∫ x³ sin x⁴ dx

35

Evaluate the following integrals:

36

Evaluate the following integrals:

∫ x³ sin (x⁴ + 1) dx

37

Evaluate the following integrals:

38

Evaluate the following integrals:

39

Evaluate the following integrals:

∫ 2x sec³ (x² + 3) tan (x² + 3) dx

40

Evaluate the following integrals:

41

Evaluate the following integrals:

42

Evaluate the following integrals:

43

Evaluate the following integrals:

44

Evaluate the following integrals:

∫ sec⁴ x tan x dx

45

Evaluate the following integrals:

46

Evaluate the following integrals:

47

Evaluate the following integrals:

48

Evaluate the following integrals:

49

Evaluate the following integrals:

50

Evaluate the following integrals:

51

Evaluate the following integrals:

52

Evaluate the following integrals:

53

Evaluate the following integrals:

54

Evaluate the following integrals:

55

Evaluate the following integrals:

56

Evaluate the following integrals:

57

Evaluate the following integrals:

58

Evaluate the following integrals:

59

Evaluate the following integrals:

60

Evaluate the following integrals:

61

Evaluate the following integrals:

62

Evaluate the following integrals:

∫ tan³2x sec 2x dx

63

Evaluate the following integrals:

64

Evaluate the following integrals:

65

Evaluate the following integrals:

66

Evaluate the following integrals:

67

Evaluate the following integrals:

68

Evaluate the following integrals:

69

Evaluate the following integrals:

70

Evaluate the following integrals:

71

Evaluate the following integrals:

72

Evaluate the following integrals:

Exercise 19.10

1

2

3

4

5

6

7

8

∫ x(1 – x)²³ dx

9

10

Exercise 19.11

1

Evaluate the following integrals:

∫ tan³ x sec² x dx

2

Evaluate the following integrals:

∫ tan x sec⁴ x dx

3

Evaluate the following integrals:

∫ tan⁵ x sec⁴ x dx

4

Evaluate the following integrals:

∫ sec⁶ x tan x dx

5

Evaluate the following integrals:

∫ tan⁵ x dx

6

Evaluate the following integrals:

7

Evaluate the following integrals:

∫ sec⁴ 2x dx

8

Evaluate the following integrals:

∫ cosec⁴ 3x dx

9

Evaluate the following integrals:

∫ cotⁿ x cosec² x dx, n ≠ –1

10

Evaluate the following integrals:

∫ cot⁵ x cosec⁴ x dx

11

Evaluate the following integrals:

∫ cot⁵ x dx

12

Evaluate the following integrals:

∫ cot⁶ x dx

Exercise 19.12

1

Evaluate the following integrals:

∫ sin⁴ x cos³ x dx

2

Evaluate the following integrals:

∫ sin⁵ x dx

3

Evaluate the following integrals:

∫ cos⁵ x dx

4

Evaluate the following integrals:

∫ sin⁵ x cos x dx

5

Evaluate the following integrals:

∫ sin³ x cos⁶ x dx

6

Evaluate the following integrals:

∫ cos⁷ x dx

7

Evaluate the following integrals:

∫ x cos³ x² sin x² dx

8

Evaluate the following integrals:

∫ sin⁷ x dx

9

Evaluate the following integrals:

∫ sin³ x cos⁵ x dx

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

Exercise 19.13

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

Exercise 19.14

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

10

Evaluate the following integrals:

Exercise 19.15

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

Exercise 19.16

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

14

Evaluate the following integrals:

15

Evaluate the following integrals:

Exercise 19.17

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

Exercise 19.18

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

14

Evaluate the following integrals:

15

Evaluate the following integrals:

16

Evaluate the following integrals:

17

Evaluate the following integrals:

18

Evaluate the following integrals:

Exercise 19.19

1

Evaluate the integral:

2

Evaluate the integral:

3

Evaluate the integral:

4

Evaluate the integral:

5

Evaluate the integral:

6

Evaluate the integral:

7

Evaluate the integral:

8

Evaluate the integral:

9

Evaluate the integral:

10

Evaluate the integral:

11

Evaluate the integral:

12

Evaluate the integral:

13

Evaluate the integral:

4

Evaluate the integral:

5

Evaluate the integral:

16

Evaluate the integral:

17

Evaluate the integral:

Exercise 19.20

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

10

Evaluate the following integrals:

Exercise 19.21

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

14

Evaluate the following integrals:

15

Evaluate the following integrals:

16

Evaluate the following integrals:

17

Evaluate the following integrals:

18

Evaluate the following integrals:

Exercise 19.22

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

..

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

.w.

10

Evaluate the following integrals:

11

Evaluate the following integrals:

Exercise 19.23

1

Evaluate the following integrals:

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

7

Evaluate the following integrals:

8

Evaluate the following integrals:

9

Evaluate the following integrals:

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

14

Evaluate the following integrals:

15

Evaluate the following integrals:

Exercise 19.24

1

Evaluate the integral

2

Evaluate the integral

3

Evaluate the integral

4

Evaluate the integral

5

Evaluate the integral

6

Evaluate the integral

7

Evaluate the integral

8

Evaluate the integral

9

Evaluate the integral

10

Evaluate the integral

11

Evaluate the integral

Exercise 19.25

1

Evaluate the following integrals:

∫ x cos x dx

2

Evaluate the following integrals:

∫ log (x + 1) dx

3

Evaluate the following integrals:

∫ x³ log x dx

4

Evaluate the following integrals:

∫ xe^x dx

5

Evaluate the following integrals:

∫ xe^2x dx

6

Evaluate the following integrals:

∫ x² e^–x dx

7

Evaluate the following integrals:

∫ x² cos x dx

8

Evaluate the following integrals:

∫ x² cos 2x dx

9

Evaluate the following integrals:

∫ x sin 2x dx

10

Evaluate the following integrals:

11

Evaluate the following integrals:

∫ x² cos x dx

12

Evaluate the following integrals:

∫ x cosec² x dx

13

Evaluate the following integrals:

∫ x cos² x dx

14

Evaluate the following integrals:

∫ xⁿ log x dx

15

Evaluate the following integrals:

16

Evaluate the following integrals:

∫ x² sin² x dx

17

Evaluate the following integrals:

18

Evaluate the following integrals:

∫ x³ cos x² dx

19

Evaluate the following integrals:

∫ x sin x cos x dx

20

Evaluate the following integrals:

∫ sin x log (cos x) dx

21

Evaluate the following integrals:

∫ (log x)² x dx

22

Evaluate the following integrals:

23

Evaluate the following integrals:

24

Evaluate the following integrals:

25

Evaluate the following integrals:

∫ log₁₀ x dx

26

Evaluate the following integrals:

∫ cos √x dx

27

Evaluate the following integrals:

28

Evaluate the following integrals:

29

Evaluate the following integrals:

∫ cosec³ x dx

30

Evaluate the following integrals:

∫ sec^–1 √x dx

31

Evaluate the following integrals:

∫ sin^–1 √x dx

32

Evaluate the following integrals:

∫ x tan² x dx

33

Evaluate the following integrals:

34

Evaluate the following integrals:

∫ (x + 1)e^x log(xe^x) dx

35

Evaluate the following integrals:

∫ sin^–1 (3x – 4x³) dx

36

Evaluate the following integrals:

37

Evaluate the following integrals:

38

Evaluate the following integrals:

∫ x² sin^–1 x dx

39

Evaluate the following integrals:

40

Evaluate the following integrals:

41

Evaluate the following integrals:

∫ cos^–1 (4x³ – 3x) dx

42

Evaluate the following integrals:

43

Evaluate the following integrals:

44

Evaluate the following integrals:

∫ (x + 1) log x dx

45

Evaluate the following integrals:

∫ x² tan^–1 x dx

46

Evaluate the following integrals:

∫ (e^{log x} + sin x) cos x dx

47

Evaluate the following integrals:

48

Evaluate the following integrals:

∫ tan^–1 (√x) dx

49

Evaluate the following integrals:

∫ x³ tan^–1 x dx

50

Evaluate the following integrals:

∫ x sin x cos 2x dx

51

Evaluate the following integrals:

∫ (tan^–1 x²) x dx

52

Evaluate the following integrals:

53

Evaluate the following integrals:

∫ sin³ √x dx

54

Evaluate the following integrals:

∫ x sin³ x dx

55

Evaluate the following integrals:

∫ cos³ √x dx

56

Evaluate the following integrals:

∫ x cos³ x dx

57

Evaluate the following integrals:

58

Evaluate the following integrals:

59

Evaluate the following integrals:

60

Evaluate the following integrals:

Exercise 19.26

1

Evaluate the following integrals:

∫ e^x (cos x – sin x) dx

2

Evaluate the following integrals:

3

Evaluate the following integrals:

4

Evaluate the following integrals:

∫ e^x (cot x – cosec² x) dx

5

Evaluate the following integrals:

6

Evaluate the following integrals:

∫ e^x sec x (1 + tan x) dx

7

Evaluate the following integrals:

∫ e^x (tan x – log cos x) dx

8

Evaluate the following integrals:

∫ e^x [sec x + log (sec x + tan x)] dx

9

Evaluate the following integrals:

∫ e^x (cot x + log sin x) dx

10

Evaluate the following integrals:

11

Evaluate the following integrals:

12

Evaluate the following integrals:

13

Evaluate the following integrals:

14

Evaluate the following integrals:

15

Evaluate the following integrals:

16

Evaluate the following integrals:

17

Evaluate the following integrals:

18

Evaluate the following integrals:

19

Evaluate the following integrals:

∫ e^2x (– sin x + 2 cos x) dx

20

Evaluate the following integrals:

21

Evaluate the following integrals:

22

Evaluate the following integrals:

∫ {tan (log x) + sec² (log x)} dx

23

Evaluate the following integrals:

24

Evaluate the following integrals:

Exercise 19.27

1

Evaluate the following integrals:

∫ e^ax cos bx dx

2

Evaluate the following integrals:

∫ e^ax sin (bx + c) dx

3

Evaluate the following integrals:

∫ cos (log x) dx

4

Evaluate the following integrals:

∫ e^2x cos (3x + 4) dx

5

Evaluate the following integrals:

∫ e^2x sin x cos x dx

6

Evaluate the following integrals:

e^2x sin x dx

7

Evaluate the following integrals:

∫ e^2x sin (3x + 1) dx

8

Evaluate the following integrals:

∫ e^x sin² x dx

9

Evaluate the following integrals:

10

Evaluate the following integrals:

∫ e^2x cos² x dx

11

Evaluate the following integrals:

∫ e^–2x sin x dx

12

Evaluate the following integrals:

Exercise 19.28

1

Evaluate the integral:

2

Evaluate the integral:

3

Evaluate the integral:

4

Evaluate the integral:

5

Evaluate the integral:

6

Evaluate the integral:

7

Evaluate the integral:

8

Evaluate the integral:

9

Evaluate the integral:

10

Evaluate the integral:

11

Evaluate the integral:

12

Evaluate the integral:

13

Evaluate the integral:

14

Evaluate the integral:

15

Evaluate the integral:

16

Evaluate the integral:

17

Evaluate the integral:

18

Evaluate the integral:

Exercise 19.29

1

Evaluate the following integrals –

2

Evaluate the following integrals –

3

Evaluate the following integrals –

4

Evaluate the following integrals –

5

Evaluate the following integrals –

6

Evaluate the following integrals –

7

Evaluate the following integrals –

8

Evaluate the following integrals –

9

Evaluate the following integrals –

10

Evaluate the following integrals –

11

Evaluate the following integrals –

12

Evaluate the following integrals –

13

Evaluate the following integrals –

14

Evaluate the following integrals –

Exercise 19.30

1

Evaluate the following integral:

2

Evaluate the following integral:

3

Evaluate the following integral:

4

Evaluate the following integral:

5

Evaluate the following integral:

6

Evaluate the following integral:

7

Evaluate the following integral:

8

Evaluate the following integral:

9

Evaluate the following integral:

10

Evaluate the following integral:

11

Evaluate the following integral:

12

Evaluate the following integral:

13

Evaluate the following integral:

14

Evaluate the following integral:

15

Evaluate the following integral:

, where a, b, c are distinct.

16

Evaluate the following integral:

17

Evaluate the following integral:

18

Evaluate the following integral:

19

Evaluate the following integral:

20

Evaluate the following integral:

21

Evaluate the following integral:

22

Evaluate the following integral:

23

Evaluate the following integral:

24

Evaluate the following integral:

25

Evaluate the following integral:

26

Evaluate the following integral:

27

Evaluate the following integral:

28

Evaluate the following integral:

29

Evaluate the following integral:

dx

30

Evaluate the following integral:

dx

31

Evaluate the following integral:

dx

32

Evaluate the following integral:

dx

33

Evaluate the following integral:

34

Evaluate the following integral:

35

Evaluate the following integral:

36

Evaluate the following integral:

37

Evaluate the following integral:

38

Evaluate the following integral:

39

Evaluate the following integral:

40

Evaluate the following integral:

41

Evaluate the following integral:

42

Evaluate the following integral:

43

Evaluate the following integral:

44

Evaluate the following integral:

45

Evaluate the following integral:

dx

46

Evaluate the following integral:

47

Evaluate the following integral:

48

Evaluate the following integral:

49

Evaluate the following integral:

50

Evaluate the following integral:

51

Evaluate the following integral:

52

Evaluate the following integral:

53

Evaluate the following integral:

54

Evaluate the following integral:

55

Evaluate the following integral:

56

Evaluate the following integral:

57

Evaluate the following integral:

58

Evaluate the following integral:

59

Evaluate the following integral:

60

Evaluate the following integral:

61

Evaluate the following integral:

62

Evaluate the following integral:

63

Evaluate the following integral:

64

Evaluate the following integral:

65

Evaluate the following integral:

66

Evaluate the following integral:

67

Evaluate the following integral:

68

Evaluate the following integral:

69

Evaluate the following integral:

Exercise 19.31

1

Evaluate the following integral:

2

Evaluate the following integral:

3

Evaluate the following integral:

4

Evaluate the following integral:

5

Evaluate the following integral:

6

Evaluate the following integral:

7

Evaluate the following integral:

8

Evaluate the following integral:

9

Evaluate the following integral:

10

Evaluate the following integral:

11

Evaluate the following integral:

Exercise 19.32

1

Evaluate the following integral:

2

Evaluate the following integral:

3

Evaluate the following integral:

4

Evaluate the following integral:

5

Evaluate the following integral:

6

Evaluate the following integral:

7

Evaluate the following integral:

8

Evaluate the following integral:

9

Evaluate the following integral:

10

Evaluate the following integral:

11

Evaluate the following integral:

12

Evaluate the following integral:

13

Evaluate the following integral:

14

Evaluate the following integral:

Very short answer

16

Write a value of

17

Write a value of

18

Write a value of

19

Write a value of

20

Write a value of

21

Write a value of

22

Write a value of

23

Write a value of

24

Write a value of

25

Write a value of

26

Write a value of

27

Write a value of

28

Write a value of

29

Write a value of

30

Write a value of

31

Write a value of

32

Write a value of s

33

Write a value of

34

Write a value of

35

Write a value of

36

Write a value of

37

Write a value of

38

Evaluate:

39

Evaluate:

40

Evaluate:

41

42

Evaluate:

43

Evaluate:

44

Evaluate:

45

Evaluate:

1

Write a value of

2

Write a value of

3

Write a value of

4

Write a value of

5

Write a value of

6

Write a value of

7

Write a value of

8

Write a value of

9

Write a value of

10

Write a value of

11

Write a value of

12

Write a value of

13

Write a value of

14

Write a value of

15

Write a value of

46

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Evaluate:

48

Evaluate:

49

Evaluate:

50

Evaluate:

51

Evaluate:

52

Evaluate:

53

Evaluate:

54

Evaluate:

55

Evaluate:

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If then write the value of f(x).

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If then write the value f(x).

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Evaluate:

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Write the anti-derivative of

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Evaluate:

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Evaluate:

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Evaluate:

MCQ

18

Mark the correct alternative in each of the following:

18

Mark the correct alternative in each of the following:

19

Mark the correct alternative in each of the following:

Evaluate

19

Mark the correct alternative in each of the following:

Evaluate

20

Mark the correct alternative in each of the following:

Evaluate

20

Mark the correct alternative in each of the following:

Evaluate

21

Mark the correct alternative in each of the following:

Evaluate

21

Mark the correct alternative in each of the following:

Evaluate

22

Mark the correct alternative in each of the following:

Evaluate

22

Mark the correct alternative in each of the following:

Evaluate

23

Mark the correct alternative in each of the following:

Evaluate

23

Mark the correct alternative in each of the following:

Evaluate

24

Mark the correct alternative in each of the following:

The primitive of the function is

24

Mark the correct alternative in each of the following:

The primitive of the function is

25

Mark the correct alternative in each of the following:

The value of is

25

Mark the correct alternative in each of the following:

The value of is

26

Mark the correct alternative in each of the following:

is equal to

26

Mark the correct alternative in each of the following:

is equal to

27

Mark the correct alternative in each of the following:

27

Mark the correct alternative in each of the following:

28

Mark the correct alternative in each of the following:

The value of is equal to

28

Mark the correct alternative in each of the following:

The value of is equal to

29

Mark the correct alternative in each of the following:

If then α is equal to

29

Mark the correct alternative in each of the following:

If then α is equal to

30

Mark the correct alternative in each of the following:

30

Mark the correct alternative in each of the following:

31

Mark the correct alternative in each of the following:

is equal to

31

Mark the correct alternative in each of the following:

is equal to

32

Mark the correct alternative in each of the following:

is equal to

32

Mark the correct alternative in each of the following:

is equal to

33

Mark the correct alternative in each of the following:

then

33

Mark the correct alternative in each of the following:

then

34

Mark the correct alternative in each of the following:

34

Mark the correct alternative in each of the following:

35

Mark the correct alternative in each of the following:

If a log |1 + x² +b tan^–1

then

35

Mark the correct alternative in each of the following:

If a log |1 + x² +b tan^–1

then

Revision exercise

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Evaluate .

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Evaluate