RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 20. Indefinite Integrals

Subject: Maths - Class 12th

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

Chapter Exercises

Exercise 20.1
Exercise 20.2
Exercise 20.3
Exercise 20.4
Exercise 20.5
Exercise 20.6
Very short answer
MCQ

Exercise 20.1

1

Evaluate the following definite integrals:
2

Evaluate the following definite integrals:
3

Evaluate the following definite integrals:
4

Evaluate the following definite integrals:
5

Evaluate the following definite integrals:
6

Evaluate the following definite integrals:
7

Evaluate the following definite integrals:
8

Evaluate the following definite integrals:
9

Evaluate the following definite integrals:
10

Evaluate the following definite integrals:
11

Evaluate the following definite integrals:
12

Evaluate the following definite integrals:
13

Evaluate the following definite integrals:
14

Evaluate the following definite integrals:
15

Evaluate the following definite integrals:
16

Evaluate the following definite integrals:
17

Evaluate the following definite integrals:
18

Evaluate the following definite integrals:
19

Evaluate the following definite integrals:
20

Evaluate the following definite integrals:
21

Evaluate the following definite integrals:
22

Evaluate the following definite integrals:
23

Evaluate the following definite integrals:
24

Evaluate the following definite integrals:
25

Evaluate the following definite integrals:
26

Evaluate the following definite Integrals:
27

Evaluate the following definite Integrals:
28

Evaluate the following definite Integrals:
29

Evaluate the following definite Integrals:
30

Evaluate the following definite Integrals:
31

Evaluate the following definite Integrals:
32

Evaluate the following definite Integrals:
33

Evaluate the following definite Integrals:
34

Evaluate the following definite Integrals:
35

Evaluate the following definite Integrals:
36

Evaluate the following definite Integrals:
37

Evaluate the following definite Integrals:
38

Evaluate the following definite Integrals:
39

Evaluate the following definite Integrals:
40

Evaluate the following definite Integrals:
41

Evaluate the following definite Integrals:
42

Evaluate the following definite Integrals:
43

Evaluate the following definite Integrals:
44

Evaluate the following definite Integrals:
45

Evaluate the following definite Integrals:
46

Evaluate the following definite Integrals:
47

Evaluate the following definite Integrals:
48

Evaluate the following definite Integrals:
49

Evaluate the following definite Integrals:
50

Evaluate the following definite Integrals:
51

Evaluate the following definite Integrals:
52

Evaluate the following definite Integrals:
53

Evaluate the following definite Integrals:
54

Evaluate the following definite Integrals:
55

Evaluate the following definite Integrals:
56

Evaluate the following definite Integrals:
57

Evaluate the following definite Integrals:
58

Evaluate the following definite Integrals:
59

Evaluate the following definite Integrals:
60

If find value of k
61

If find the value of a.
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:

Exercise 20.2

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:
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:

Exercise 20.3

1

Evaluate the following Integrals:

where

1

Evaluate the following Integrals:

where

1

Evaluate the following Integrals:

where

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:

where

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:

Exercise 20.4

1

Evaluate of each of the following integral:
2

Evaluate of each of the following integral:
3

Evaluate of each of the following integral:
4

Evaluate of each of the following integral:
5

Evaluate of each of the following integral:
6

Evaluate of each of the following integral:
7

Evaluate of each of the following integral:
8

Evaluate of each of the following integral:

.
9

Evaluate of each of the following integral:
10

Evaluate of each of the following integral:

, n ∈ N, n ≥ 2
11

Evaluate of each of the following integral:
12

Evaluate of each of the following integral:
13

Evaluate of each of the following integral:
14

Evaluate of each of the following integral:
15

Evaluate of each of the following integral:
16

If f(a + b – x) = f(x), then prove that

Exercise 20.5

1

Evaluate the following integral:

dx
1

Evaluate the following integral:

dx
2

Evaluate the following integral:

dx
2

Evaluate the following integral:

dx
3

Evaluate the following integral:

dx
3

Evaluate the following integral:

dx
4

Evaluate the following integral:

dx
4

Evaluate the following integral:

dx
5

Evaluate the following integral:

dx
5

Evaluate the following integral:

dx
6

Evaluate the following integral:

dx
6

Evaluate the following integral:

dx
7

Evaluate the following integral:
7

Evaluate the following integral:
8

Evaluate the following integral:
8

Evaluate the following integral:
9

Evaluate the following integral:
9

Evaluate the following integral:
10

Evaluate the following integral:
10

Evaluate the following integral:
11

Evaluate the following integral:
11

Evaluate the following integral:
12

Evaluate the following integral:
12

Evaluate the following integral:
13

Evaluate the following integral:
13

Evaluate the following integral:
14

Evaluate the following integral:
14

Evaluate the following integral:
15

Evaluate the following integral:
15

Evaluate the following integral:
16

Evaluate the following integral:

, 0 < α < π
16

Evaluate the following integral:

, 0 < α < π
17

Evaluate the following integral:
17

Evaluate the following integral:
18

Evaluate the following integral:
18

Evaluate the following integral:
19

Evaluate the following integral:
19

Evaluate the following integral:
20

Evaluate the following integral:
20

Evaluate the following integral:
21

Evaluate the following integral:
21

Evaluate the following integral:
22

Evaluate the following integral:
22

Evaluate the following integral:
23

Evaluate the following integral:
23

Evaluate the following integral:
24

Evaluate the following integral:
24

Evaluate the following integral:
25

Evaluate the following integral:
25

Evaluate the following integral:
26

Evaluate the following integral:
26

Evaluate the following integral:
27

Evaluate the following integral:
27

Evaluate the following integral:
28

Evaluate the following integral:
28

Evaluate the following integral:
29

Evaluate the following integral:
29

Evaluate the following integral:
30

Evaluate the following integral:
30

Evaluate the following integral:
31

Evaluate the following integral:
31

Evaluate the following integral:
32

Evaluate the following integral:
32

Evaluate the following integral:
33

Evaluate the following integral:
33

Evaluate the following integral:
34

Evaluate the following integral:
34

Evaluate the following integral:
35

Evaluate the following integral:

dx
35

Evaluate the following integral:

dx
36

evaluate:
36

evaluate:
37

37

38

38

39

evaluate:
39

evaluate:
40

evaluate:
40

evaluate:
41

evaluate:
41

evaluate:
42

evaluate:
42

evaluate:
43

If f is an integrable function such that f(2a – x) = f(x), then prove that
43

If f is an integrable function such that f(2a – x) = f(x), then prove that
44

if prove that

44

if prove that

45

If f is an integrable function, show that

(i)


(ii)

45

If f is an integrable function, show that

(i)


(ii)

46

If f(x) is a continuous function defined on [0,2a]. Then Prove that
46

If f(x) is a continuous function defined on [0,2a]. Then Prove that
47

If f(a + b – x) = f(x) prove that:
47

If f(a + b – x) = f(x) prove that:
48

If f(x) is a continuous function defined on [ – a,a] ,then prove that
48

If f(x) is a continuous function defined on [ – a,a] ,then prove that
49

Prove that:
49

Prove that:

Exercise 20.6

1

Evaluate the following integrals as a limit of sums:
2

Evaluate the following integrals as a limit of sums:
3

Evaluate the following integrals as a limit of sums:
4

Evaluate the following integrals as a limit of sums:
5

Evaluate the following integrals as a limit of sums:
6

Evaluate the following integrals as a limit of sums:
7

Evaluate the following integrals as a limit of sums:
8

Evaluate the following integrals as a limit of sums:
9

Evaluate the following integrals as a limit of sums:
10

Evaluate the following integrals as a limit of sums:
11

Evaluate the following integrals as a limit of sums:
12

Evaluate the following integrals as a limit of sums:
13

Evaluate the following integrals as a limit of sums:
14

Evaluate the following integrals as a limit of sums:
15

Evaluate the following integrals as a limit of sums:
16

Evaluate the following integrals as a limit of sums:
17

Evaluate the following integrals as a limit of sums:
18

Evaluate the following integrals as a limit of sums:
19

Evaluate the following integrals as a limit of sums:
20

Evaluate the following integrals as a limit of sums:
21

Evaluate the following integrals as a limit of sums:
22

Evaluate the following integrals as a limit of sums:
23

Evaluate the following integrals as a limit of sums:
24

Evaluate the following integrals as a limit of sums:
25

Evaluate the following integrals as a limit of sums:
26

Evaluate the following integrals as a limit of sums:
27

Evaluate the following integrals as a limit of sums:
28

Evaluate the following integrals as a limit of sums:
29

Evaluate the following integrals as a limit of sums:
30

Evaluate the following integrals as a limit of sums:
31

Evaluate the following integrals as a limit of sums:
32

Evaluate the following integrals as a limit of sums:
33

Evaluate the following integrals as a limit of sums:

Very short answer

1

Evaluate

2

Evaluate

3

Evaluate

4

Evaluate
5

Evaluate

6

Evaluate
7

Evaluate

8

Evaluate

9

Evaluate
10

Evaluate
11

Evaluate
12

Evluate
13

Evaluate
14

Evaluate
15

Evaluate

16

Evaluate
17

Evaluate

18

Evaluate
19

Evaluate

20

Evaluate

21

Evaluate

22

Evaluate

23

Evaluate

24

Evaluate
25

Evaluate

26

Evaluate

27

Evaluate
28

Evaluate

29

Evaluate
30

Evaluate

31

If find the value of k.
32

If write the value of a.
33

If then write the value of f’(x).
34

If find the value of a.
35

Write the coefficient a, b, c of which the value of the integral is independent.
36

Evaluate

37

I =
38

I =
39

I =
40

I=
41

I =
42

I =
43

I =
44

I =
45

I =

MCQ

1

equals
2

equals
3

4

The value of is
5

The value of the integral is
6

equals
7

equals
8

equals
9

equals
10

11

12

is
13

Given that = the value of is
14

15

is equal to
16

17

The value of the integral is
18

dx is equal to
19

is equal to
20

The value of is
21

If then a equals
22

If then equals
23

The value of is
24

is equal to
25

is equal to
26

The derivative of f(x) = is
27

If sin x dx, then the value of I10 + 90I8 is
28

29

is equal to
30

The value of the integral is
31

is equal to
32

equals to
33

is equal to
34

is equal to
35

is equal to
36

The value of is
37

38

is equal to
39

If f(a + b – x) = f(x), then is equal to
40

The value of is
41

The value of is
42

The value of is