Xii Definite Integrals Assignment
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ASSIGNMENT CLASS XII DEFINITE INTEGRALS
Evaluate the following: 2
1.
4 3
2.
cos x dx
0
2
0
6.
2
1 13. dx 5 4cos x 0
14.
1
ex 17. dx 1 e2 x 0 2
21.
18.
2
dx 22.
26.
0
2
0
0
30.
sin n x dx 34. sin n x cos n x
2 32
1 x
1 dx 2 cos x 4 sin x
tan 1 x dx 1 x 2
11.
2
x 0
cos 2 x dx
2
15.
0
2
cos 4 x dx
12.
19.
cos x dx
16.
sec 4 x dx
20.
0
1
e
x
24.
dx
1
2
sin x dx sin x cos x
28.
35.
2
32.
1 x 2 42. cos dx 2 1 x 0
1 46. dx 2 9 x
4
x sin x dx
2 x 1 log 2 x dx 2
43.
0
1 dx 1 cot x
36.
ax dx a x
a
1 2x 40. sin 1 dx 2 1 x 0
44.
x tan 1 x
0
2
1
1 x2 47. x dx 1 x 2 0
Downloaed from www.amitbajajmaths.blogspot.com
sin 2 x dx sin x cos x
a
3
1
39.
0
4
0
1
sin x cos x dx
2
4
sin 2 x log tan x dx
x0 x0
2
2 x 1 dx
0
2
sin 2 x dx x cos 4 x
1 2 x f ( x) 1 2 x
f ( x) dx, where
1
31.
4
1 x dx 1 x
0
1
x dx 3 x x
sin 1
1
27.
tan x cot x dx
2
cos x dx 3cos x sin x
0
23.
0
4
1
2
x 1 8. 2 e x dx 1 x
0
1
log 1 x 41. dx 1 x2 0
2
1
x tan x 1 2 0 sec x cos ecx dx 38. 0 cot 1 x x dx 1
0
cos 2 x log sin x dx
2x dx 2 1
5x
2
dx
2 x dx
1
45.
2
sin x dx
4
37.
sin 1 x
0
4
33.
2
2
x dx
x2 2x 3
4.
4
0
3
29.
1
7.
1
25.
0
1
x 1 log x
0
1
dx
2
1 1 x 1 x 2 dx
cos dx 10. 1 sin 2 sin
1
1
0
2
log x 1 x2 dx
9.
3.
1 sin 2x dx
0
2
5.
4
48.
2 32
1 x 1
1 tan 0
2
3
x
dx
a
1
49.
x 1 x
5
50.
dx
x
2
a x
0
0
1 2
dx
51.
54. If
5
a
2
x
2
b
2
dx
52.
0
x
x cos dx 4 2
a 1
x dx 2a sin 3 x dx , find the value of
e 0
2
a
x x 2 x 5 dx
2
0
0
53.
x
2
1
0
x dx .
a
Evaluate the following integrals as limit of sums: 2
55.
2 x 1 dx
56.
2
2 x 1 dx
x
57.
2
0
3
60.
4
3 2
3 dx
2x
1 dx
61.
2
2x
5 dx
59.
1
0
3
2
58.
3 2
x
2
x dx
1
b
2x
2
3x 5 dx
62. e x dx
0
a
ANSWERS 1.
2 3
2.
2 1
7.
1 1 log 2 4 8 4
8.
13.
3
14.
18.
1 32 12
19.
4 3
20.
1 log 2
2 1
33.
log 2 2
43.
4
44. 2
50.
4
51.
4.
4 9. log 3
3 5 1 log 5 2
38.
56. 10
e2 e 2
1 2
26. 5 2 3
25. 3
32.
5 3 3 3. log 1 3
27.
4
10.
40.
4
5.
1 e log 2 2
1 log 2 4 2
11.
6.
3 16
3 1 log 3 20 10
16.
21.
log 2 1 log 2
22. 2
23. 2e 2
29. 2 2
30.
5 2
28. 4
2
2
17. tan 1 e
4 24. 4
1 2
36. a
35. 0
3 1 log 2 log 5 2 2
12.
15.
34. 0
39. 0
45.
1 log 6 5
37.
31.
4
1 42
2 4
log 2 2
41.
log 2 8
42.
log 2 2
3
47.
1 4 2
48.
4
49.
54.
1 or 2 2
55. 6
46.
3 2 2 52. e 1 2ab a b 5 26 82 38 57. 58. 59. 3 3 3
Downloaed from www.amitbajajmaths.blogspot.com
53. 60.
41 3
63 2
61.
93 2
62. eb e a
Evaluate the following: 2
1.
4 3
2.
cos x dx
0
2
0
6.
2
1 13. dx 5 4cos x 0
14.
1
ex 17. dx 1 e2 x 0 2
21.
18.
2
dx 22.
26.
0
2
0
0
30.
sin n x dx 34. sin n x cos n x
2 32
1 x
1 dx 2 cos x 4 sin x
tan 1 x dx 1 x 2
11.
2
x 0
cos 2 x dx
2
15.
0
2
cos 4 x dx
12.
19.
cos x dx
16.
sec 4 x dx
20.
0
1
e
x
24.
dx
1
2
sin x dx sin x cos x
28.
35.
2
32.
1 x 2 42. cos dx 2 1 x 0
1 46. dx 2 9 x
4
x sin x dx
2 x 1 log 2 x dx 2
43.
0
1 dx 1 cot x
36.
ax dx a x
a
1 2x 40. sin 1 dx 2 1 x 0
44.
x tan 1 x
0
2
1
1 x2 47. x dx 1 x 2 0
Downloaed from www.amitbajajmaths.blogspot.com
sin 2 x dx sin x cos x
a
3
1
39.
0
4
0
1
sin x cos x dx
2
4
sin 2 x log tan x dx
x0 x0
2
2 x 1 dx
0
2
sin 2 x dx x cos 4 x
1 2 x f ( x) 1 2 x
f ( x) dx, where
1
31.
4
1 x dx 1 x
0
1
x dx 3 x x
sin 1
1
27.
tan x cot x dx
2
cos x dx 3cos x sin x
0
23.
0
4
1
2
x 1 8. 2 e x dx 1 x
0
1
log 1 x 41. dx 1 x2 0
2
1
x tan x 1 2 0 sec x cos ecx dx 38. 0 cot 1 x x dx 1
0
cos 2 x log sin x dx
2x dx 2 1
5x
2
dx
2 x dx
1
45.
2
sin x dx
4
37.
sin 1 x
0
4
33.
2
2
x dx
x2 2x 3
4.
4
0
3
29.
1
7.
1
25.
0
1
x 1 log x
0
1
dx
2
1 1 x 1 x 2 dx
cos dx 10. 1 sin 2 sin
1
1
0
2
log x 1 x2 dx
9.
3.
1 sin 2x dx
0
2
5.
4
48.
2 32
1 x 1
1 tan 0
2
3
x
dx
a
1
49.
x 1 x
5
50.
dx
x
2
a x
0
0
1 2
dx
51.
54. If
5
a
2
x
2
b
2
dx
52.
0
x
x cos dx 4 2
a 1
x dx 2a sin 3 x dx , find the value of
e 0
2
a
x x 2 x 5 dx
2
0
0
53.
x
2
1
0
x dx .
a
Evaluate the following integrals as limit of sums: 2
55.
2 x 1 dx
56.
2
2 x 1 dx
x
57.
2
0
3
60.
4
3 2
3 dx
2x
1 dx
61.
2
2x
5 dx
59.
1
0
3
2
58.
3 2
x
2
x dx
1
b
2x
2
3x 5 dx
62. e x dx
0
a
ANSWERS 1.
2 3
2.
2 1
7.
1 1 log 2 4 8 4
8.
13.
3
14.
18.
1 32 12
19.
4 3
20.
1 log 2
2 1
33.
log 2 2
43.
4
44. 2
50.
4
51.
4.
4 9. log 3
3 5 1 log 5 2
38.
56. 10
e2 e 2
1 2
26. 5 2 3
25. 3
32.
5 3 3 3. log 1 3
27.
4
10.
40.
4
5.
1 e log 2 2
1 log 2 4 2
11.
6.
3 16
3 1 log 3 20 10
16.
21.
log 2 1 log 2
22. 2
23. 2e 2
29. 2 2
30.
5 2
28. 4
2
2
17. tan 1 e
4 24. 4
1 2
36. a
35. 0
3 1 log 2 log 5 2 2
12.
15.
34. 0
39. 0
45.
1 log 6 5
37.
31.
4
1 42
2 4
log 2 2
41.
log 2 8
42.
log 2 2
3
47.
1 4 2
48.
4
49.
54.
1 or 2 2
55. 6
46.
3 2 2 52. e 1 2ab a b 5 26 82 38 57. 58. 59. 3 3 3
Downloaed from www.amitbajajmaths.blogspot.com
53. 60.
41 3
63 2
61.
93 2
62. eb e a
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