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Final Revision Sheet For Board 2020: DX X+ X XDX e DX e

1. This document contains 33 definite integration problems to evaluate integrals from 0 to π, 0 to 1, or other bounds. 2. The integrals involve common trigonometric, logarithmic, and other functions including sin, cos, tan, cot, sec, etc. 3. The problems cover a wide range of integration techniques like substitution, trigonometric identities, and evaluating limits of sums to find definite integrals.

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49 views1 page

Final Revision Sheet For Board 2020: DX X+ X XDX e DX e

1. This document contains 33 definite integration problems to evaluate integrals from 0 to π, 0 to 1, or other bounds. 2. The integrals involve common trigonometric, logarithmic, and other functions including sin, cos, tan, cot, sec, etc. 3. The problems cover a wide range of integration techniques like substitution, trigonometric identities, and evaluating limits of sums to find definite integrals.

Uploaded by

sekharsudhansu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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FINAL REVISION SHEET FOR BOARD 2020

DEFINITE INTEGRATION
dx ln3
ex + 1

1
1.
0
2x + 3
19. 0
2
e2 x + 1
dx

 ( )
1
dx
2.
0
2
tan x + cot x dx 20.  (1 − 2 x )
0
2
2
1 − x2

3.  2
log sin x dx 

  sin
0 2 7
21. x dx
 cot (1− x + x ) dx
1 −
−1 2 2
4.
0 

a a−x 22.  2
sin x cos x dx

0
5. dx
a+ x
  x dx , where . represents
−a 1.5
23. Evaluate
 x dx 0
6.  ( a  0, b  0 ) the greatest integer function.
0 a cos + b 2 sin 2 x
2 2

24. Evaluate the value of


 x (1− x)
1 n
2
7. dx 
3 + 5cos x 

0
2
log  dx
 3 + 5sin x 

sin x + cos x 0
8.  3

sin 2 x
dx
 dx
6
x tan x
25. Evaluate  0 5 + 4 cos x
dx
9. 0 sec x + tan x dx 
sin x
 x
26. Evaluate  2

sin x + cos x
dx
10. 0
0
dx
1 + sin x 
sin x
11.  2

x + sin x
dx
27. Evaluate  2
1+ sin x cos x
0
dx
0 1 + cos x 
sin 2

sin x + cos x 28. Evaluate  2 d
0 sin  + cos 4 
12.  4
4
dx
0 9 + 16sin 2 x 

13.  2
x sin x cos x
dx
29. Evaluate  0
2
log tan x dx
0 sin 4 x + cos4 x 
30. Evaluate  2
sin 2x log tan x dx
 ( x − x) dx as the limit of a
4 0
2
14. Evaluate
1
 2x 
 sin
1
−1
sum. 31. Evaluate  2 
dx

0
 1+ x 
 log (1 + tan x ) dx
 (3x −1) dx as
4 2
15. 32. Evaluate the integral 2
0
0
 x sin x
16. 0 1 + cos 2 x
dx limit of sum

sin 2 x

sin x + cos x 33. Evaluate  2
sin x + cos x
dx
 4 0
17. dx
0 3 + sin 2 x

4
34. Evaluate  x −1 + x − 2 + x − 4  dx
 ( x2 + 3x + ex ) dx as the limit
3 0
18. Evaluate 3
0

of sum. 35. Evaluate  0


2
x cos  x dx

VIM - 389, SAILASHREE VIHAR & B.J.B NAGAR, BHUBANESWAR, 9437965964, 9338965964
1|1

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