RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 16. Definite Integrals

Subject: Maths - Class 12th

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

Chapter Exercises

Exercise 16A
Exercise 16B
Exercise 16C
Exercise 16D
Objective Questions

Exercise 16A

1

Evaluate:
2

Evaluate:
3

Evaluate:
4

Evaluate:
5

Evaluate:
6

Evaluate:
7

Evaluate:
8

Evaluate:
9

Evaluate:
10

Evaluate:
11

Evaluate:
12

Evaluate:
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:


[CBSE 2004]
26

Evaluate:
27

Evaluate:
28

Evaluate:
29

Evaluate:
30

Evaluate:
31

Evaluate:
32

Evaluate:
33

Evaluate:
34

Evaluate:
35

Evaluate:
36

Evaluate:
37

Evaluate:
38

Evaluate:
39

Evaluate:
40

Evaluate:
41

Evaluate:
42

Evaluate:
43

Evaluate:
44

Evaluate:
45

Evaluate:
46

Evaluate:
47

Evaluate:
48

Evaluate:
49

Evaluate:
50

Evaluate:
51

Evaluate:
52

Evaluate:
53

Evaluate:
54

Evaluate:
55

Evaluate:
56

Evaluate:
57

Evaluate:
58

Evaluate:
59

Evaluate:
60

Evaluate:


[CBSE 2004]
61

Evaluate:

Exercise 16B

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

25.


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

Exercise 16C

1

Prove that
2

Prove that
3 A

Prove that
3 B

Prove that
4 A

Prove that
4 B

Prove that
5

Prove that
6

Prove that
7

Prove that
8

Prove that
9

Prove that
10

Prove that
11

Prove that
12

Prove that
13

Prove that
14

Prove that
15

Prove that
16

Prove that
17

Prove that
18

Prove that
19

Prove that
20

Prove that
21

Prove that
22

Prove that
23

Prove that
24

Prove that
25

Prove that
26

Prove that
27

Prove that
28

Prove that
29

Prove that
30

31

Prove that
32

Prove that

where m is a positive integer
33

Prove that
34

Prove that
35

Prove that
36

Prove that
37

Prove that
38

Prove that
39

Prove that
40

Prove that
41

Prove that
42

Prove that
43

Prove that
44

Prove that
45

Prove that
46

Prove that
47

Prove that
48

Prove that
49

Prove that
50

Prove that
51

Prove that
52

53

Prove that
54

Prove that
55

Prove that
56

Prove that

Let


Show that


57

Prove that

Let


Show that


58

Prove that

Exercise 16D

1

Evaluate each of the following integrals as the limit of sums:
2

Evaluate each of the following integrals as the limit of sums:
3

Evaluate each of the following integrals as the limit of sums:
4

Evaluate each of the following integrals as the limit of sums:
5

Evaluate each of the following integrals as the limit of sums:
6

Evaluate each of the following integrals as the limit of sums:
7

Evaluate each of the following integrals as the limit of sums:
8

Evaluate each of the following integrals as the limit of sums:
9

Evaluate each of the following integrals as the limit of sums:
10

Evaluate each of the following integrals as the limit of sums:
11

Evaluate each of the following integrals as the limit of sums:
12

Evaluate each of the following integrals as the limit of sums:
13

Evaluate each of the following integrals as the limit of sums:
14

Evaluate each of the following integrals as the limit of sums:
15

Evaluate each of the following integrals as the limit of sums:
16

Evaluate each of the following integrals as the limit of sums:
17

Evaluate each of the following integrals as the limit of sums:

Objective Questions

1

Mark (√) against the correct answer in the following:
2

Mark (√) against the correct answer in the following:
3

Mark (√) against the correct answer in the following:
4

Mark (√) against the correct answer in the following:
5

Mark (√) against the correct answer in the following:
6

Mark (√) against the correct answer in the following:
7

Mark (√) against the correct answer in the following:
8

Mark (√) against the correct answer in the following:
9

Mark (√) against the correct answer in the following:
10

Mark (√) against the correct answer in the following:
11

Mark (√) against the correct answer in the following:
12

Mark (√) against the correct answer in the following:
13

Mark (√) against the correct answer in the following:
14

Mark (√) against the correct answer in the following:
15

Mark (√) against the correct answer in the following:
16

Mark (√) against the correct answer in the following:
17

Mark (√) against the correct answer in the following:
18

Mark (√) against the correct answer in the following:
19

Mark (√) against the correct answer in the following:
20

Mark (√) against the correct answer in the following:
21

Mark (√) against the correct answer in the following:
22

Mark (√) against the correct answer in the following:
23

Mark (√) against the correct answer in the following:
24

Mark (√) against the correct answer in the following:
25

Mark (√) against the correct answer in the following:
26

Mark (√) against the correct answer in the following:
27

Mark (√) against the correct answer in the following:
28

Mark (√) against the correct answer in the following:
29

Mark (√) against the correct answer in the following:
30

Mark (√) against the correct answer in the following:
31

Mark (√) against the correct answer in the following:
32

Mark (√) against the correct answer in the following:
33

Mark (√) against the correct answer in the following:
34

Mark (√) against the correct answer in the following:
35

Mark (√) against the correct answer in the following:
36

Mark (√) against the correct answer in the following:
37

Mark (√) against the correct answer in the following:
38

Mark (√) against the correct answer in the following:
39

Mark (√) against the correct answer in the following:
40

Mark (√) against the correct answer in the following:
41

Mark (√) against the correct answer in the following:
42

Mark (√) against the correct answer in the following:
43

Mark (√) against the correct answer in the following:
44

Mark (√) against the correct answer in the following:
45

Mark (√) against the correct answer in the following:
46

Mark (√) against the correct answer in the following:
47

Mark (√) against the correct answer in the following:
48

Mark (√) against the correct answer in the following:
49

Mark (√) against the correct answer in the following:
50

Mark (√) against the correct answer in the following:
51

Mark (√) against the correct answer in the following:
52

Mark (√) against the correct answer in the following:
53

Mark (√) against the correct answer in the following:
54

Mark (√) against the correct answer in the following:
55

Mark (√) against the correct answer in the following:
56

Mark (√) against the correct answer in the following:
57

Mark (√) against the correct answer in the following:
58

Mark (√) against the correct answer in the following:
59

Mark (√) against the correct answer in the following:
60

Mark (√) against the correct answer in the following:
61

Mark (√) against the correct answer in the following:
62

Mark (√) against the correct answer in the following:
63

Mark (√) against the correct answer in the following:
64

Mark (√) against the correct answer in the following:
65

Mark (√) against the correct answer in the following:
66

Mark (√) against the correct answer in the following:
67

Mark (√) against the correct answer in the following:
68

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

Let [x] denote the greatest integer less than or equal to x.


Then,


69

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

Let [x] denote the greatest integer less than or equal to x.


Then,


70

Mark (√) against the correct answer in the following:
71

Mark (√) against the correct answer in the following:
72

Mark (√) against the correct answer in the following:
73

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