Solutions of chapter 13. Method of Integration | RS Aggarwal - Mathematics - Class 12

RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 13. Method of Integration

Subject: Maths - Class 12^th

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Chapter Exercises

Exercise 13A

Objective Questions I

Exercise 13B

Exercise 13C

Objective Questions II

Exercise 13A

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:

i.

ii.

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:

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:

73

Evaluate the following integrals:

74

Evaluate the following integrals:

75

Evaluate the following integrals:

76

Evaluate the following integrals:

77

Evaluate the following integrals:

78

Evaluate the following integrals:

79

Evaluate the following integrals:

80

Evaluate the following integrals:

81

Evaluate the following integrals:

82

Evaluate the following integrals:

83

Evaluate the following integrals:

84

Evaluate the following integrals:

85

Evaluate the following integrals:

86

Evaluate the following integrals:

87

Evaluate the following integrals:

88

Evaluate the following integrals:

89

Evaluate the following integrals:

90

Evaluate the following integrals:

91

Evaluate the following integrals:

92

Evaluate the following integrals:

93

Evaluate the following integrals:

94

Evaluate the following integrals:

95

Evaluate the following integrals:

96

Evaluate the following integrals:

97

Evaluate the following integrals:

98

Evaluate the following integrals:

99

Evaluate the following integrals:

100

Evaluate the following integrals:

101

Evaluate the following integrals:

102

Evaluate the following integrals:

Objective Questions I

1

Mark (√) against the correct answer in each of the following:

2

Mark (√) against the correct answer in each of the following:

3

Mark (√) against the correct answer in each of the following:

4

Mark (√) against the correct answer in each of the following:

5

Mark (√) against the correct answer in each of the following:

6

Mark (√) against the correct answer in each of the following:

7

Mark (√) against the correct answer in each of the following:

8

Mark (√) against the correct answer in each of the following:

9

Mark (√) against the correct answer in each of the following:

10

Mark (√) against the correct answer in each of the following:

11

Mark (√) against the correct answer in each of the following:

12

Mark (√) against the correct answer in each of the following:

13

Mark (√) against the correct answer in each of the following:

14

Mark (√) against the correct answer in each of the following:

15

Mark (√) against the correct answer in each of the following:

16

Mark (√) against the correct answer in each of the following:

17

Mark (√) against the correct answer in each of the following:

18

Mark (√) against the correct answer in each of the following:

19

Mark (√) against the correct answer in each of the following:

20

Mark (√) against the correct answer in each of the following:

21

Mark (√) against the correct answer in each of the following:

22

Mark (√) against the correct answer in each of the following:

23

Mark (√) against the correct answer in each of the following:

24

Mark (√) against the correct answer in each of the following:

25

Mark (√) against the correct answer in each of the following:

26

Mark (√) against the correct answer in each of the following:

27

Mark (√) against the correct answer in each of the following:

28

Mark (√) against the correct answer in each of the following:

29

Mark (√) against the correct answer in each of the following:

30

Mark (√) against the correct answer in each of the following:

31

Mark (√) against the correct answer in each of the following:

32

Mark (√) against the correct answer in each of the following:

33

Mark (√) against the correct answer in each of the following:

34

Mark (√) against the correct answer in each of the following:

35

Mark (√) against the correct answer in each of the following:

36

Mark (√) against the correct answer in each of the following:

37

Mark (√) against the correct answer in each of the following:

38

Mark (√) against the correct answer in each of the following:

39

Mark (√) against the correct answer in each of the following:

40

Mark (√) against the correct answer in each of the following:

41

Mark (√) against the correct answer in each of the following:

42

Mark (√) against the correct answer in each of the following:

43

Mark (√) against the correct answer in each of the following:

44

Mark (√) against the correct answer in each of the following:

45

Mark (√) against the correct answer in each of the following:

46

Mark (√) against the correct answer in each of the following:

47

Mark (√) against the correct answer in each of the following:

48

Mark (√) against the correct answer in each of the following:

49

Mark (√) against the correct answer in each of the following:

50

Mark (√) against the correct answer in each of the following:

51

Mark (√) against the correct answer in each of the following:

52

Mark (√) against the correct answer in each of the following:

53

Mark (√) against the correct answer in each of the following:

54

Mark (√) against the correct answer in each of the following:

55

Mark (√) against the correct answer in each of the following:

56

Mark (√) against the correct answer in each of the following:

57

Mark (√) against the correct answer in each of the following:

59

Mark (√) against the correct answer in each of the following:

59

Mark (√) against the correct answer in each of the following:

60

Mark (√) against the correct answer in each of the following:

61

Mark (√) against the correct answer in each of the following:

62

Mark (√) against the correct answer in each of the following:

63

Mark (√) against the correct answer in each of the following:

64

Mark (√) against the correct answer in each of the following:

65

Mark (√) against the correct answer in each of the following:

66

Mark (√) against the correct answer in each of the following:

67

Mark (√) against the correct answer in each of the following:

68

Mark (√) against the correct answer in each of the following:

69

Mark (√) against the correct answer in each of the following:

70

Mark (√) against the correct answer in each of the following:

71

Mark (√) against the correct answer in each of the following:

72

Mark (√) against the correct answer in each of the following:

73

Mark (√) against the correct answer in each of the following:

74

Mark (√) against the correct answer in each of the following:

75

Mark (√) against the correct answer in each of the following:

76

Mark (√) against the correct answer in each of the following:

77

Mark (√) against the correct answer in each of the following:

78

Mark (√) against the correct answer in each of the following:

79

Mark (√) against the correct answer in each of the following:

80

Mark (√) against the correct answer in each of the following:

81

Mark (√) against the correct answer in each of the following:

82

Mark (√) against the correct answer in each of the following:

83

Mark (√) against the correct answer in each of the following:

84

Mark (√) against the correct answer in each of the following:

85

Mark (√) against the correct answer in each of the following:

86

Mark (√) against the correct answer in each of the following:

87

Mark (√) against the correct answer in each of the following:

88

Mark (√) against the correct answer in each of the following:

89

Mark (√) against the correct answer in each of the following:

90

Mark (√) against the correct answer in each of the following:

91

Mark (√) against the correct answer in each of the following:

92

Mark (√) against the correct answer in each of the following:

93

Mark (√) against the correct answer in each of the following:

94

Mark (√) against the correct answer in each of the following:

95

Mark (√) against the correct answer in each of the following:

96

Mark (√) against the correct answer in each of the following:

97

Mark (√) against the correct answer in each of the following:

98

Mark (√) against the correct answer in each of the following:

99

Mark (√) against the correct answer in each of the following:

100

Mark (√) against the correct answer in each of the following:

101

Mark (√) against the correct answer in each of the following:

Exercise 13B

1

Evaluate the following integrals:

(ii)

2

Evaluate the following integrals:

(i)

(ii)

3

Evaluate the following integrals:

(i)

(ii)

4

Evaluate the following integrals:

5

Evaluate the following integrals:

6

Evaluate the following integrals:

(i)

(ii)

7

Evaluate the following integrals:

(i)

(ii)

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:

a > 0 and b > 0

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:

Exercise 13C

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:

[CBSE 2006C]

43

Evaluate the following integrals:

44

Evaluate the following integrals:

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:

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:

73

Evaluate the following integrals:

74

Evaluate the following integrals:

75

Evaluate the following integrals:

76

Evaluate the following integrals:

77

Evaluate the following integrals:

78

Evaluate the following integrals:

79

Evaluate the following integrals:

80

Evaluate the following integrals:

81

Evaluate the following integrals:

82

Evaluate the following integrals:

83

Evaluate the following integrals:

84

Evaluate the following integrals:

85

Evaluate the following integrals:

86

Evaluate the following integrals:

87

Evaluate the following integrals:

Objective Questions II

1

Mark (√) against the correct answer in each of the following:

2

Mark (√) against the correct answer in each of the following:

3

Mark (√) against the correct answer in each of the following:

4

Mark (√) against the correct answer in each of the following:

5

Mark (√) against the correct answer in each of the following:

6

Mark (√) against the correct answer in each of the following:

7

Mark (√) against the correct answer in each of the following:

8

Mark (√) against the correct answer in each of the following:

9

Mark (√) against the correct answer in each of the following:

10

Mark (√) against the correct answer in each of the following:

11

Mark (√) against the correct answer in each of the following:

12

Mark (√) against the correct answer in each of the following:

13

Mark (√) against the correct answer in each of the following:

14

Mark (√) against the correct answer in each of the following:

15

Mark (√) against the correct answer in each of the following:

16

Mark (√) against the correct answer in each of the following:

17

Mark (√) against the correct answer in each of the following:

18

Mark (√) against the correct answer in each of the following:

19

Mark (√) against the correct answer in each of the following:

20

Mark (√) against the correct answer in each of the following:

21

Mark (√) against the correct answer in each of the following:

22

Mark (√) against the correct answer in each of the following:

23

Mark (√) against the correct answer in each of the following:

24

Mark (√) against the correct answer in each of the following:

25

Mark (√) against the correct answer in each of the following:

26

Mark (√) against the correct answer in each of the following:

27

Mark (√) against the correct answer in each of the following:

28

Mark (√) against the correct answer in each of the following:

29

Mark (√) against the correct answer in each of the following:

30

Mark (√) against the correct answer in each of the following:

31

Mark (√) against the correct answer in each of the following:

32

Mark (√) against the correct answer in each of the following:

33

Mark (√) against the correct answer in each of the following:

34

Mark (√) against the correct answer in each of the following:

35

Mark (√) against the correct answer in each of the following:

36

Mark (√) against the correct answer in each of the following:

37

Mark (√) against the correct answer in each of the following:

38

Mark (√) against the correct answer in each of the following:

39

Mark (√) against the correct answer in each of the following:

40

Mark (√) against the correct answer in each of the following:

41

Mark (√) against the correct answer in each of the following:

42

Mark (√) against the correct answer in each of the following:

43

Mark (√) against the correct answer in each of the following:

44

Mark (√) against the correct answer in each of the following:

45

Mark (√) against the correct answer in each of the following:

46

Mark (√) against the correct answer in each of the following:

47

Mark (√) against the correct answer in each of the following:

48

Mark (√) against the correct answer in each of the following:

49

Mark (√) against the correct answer in each of the following:

50

Mark (√) against the correct answer in each of the following:

51

Mark (√) against the correct answer in each of the following:

52

Mark (√) against the correct answer in each of the following:

53

Mark (√) against the correct answer in each of the following:

54

Mark (√) against the correct answer in each of the following:

55

Mark (√) against the correct answer in each of the following:

56

Mark (√) against the correct answer in each of the following: