#### Integral Calculus Important Questions Paper

11th Standard

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Mathematics

All questions are compulsory.
Time : 01:00:00 Hrs
Total Marks : 50

Part A

10 x 1 = 10
1. If $\int {3^{1\over x}\over x^2}dx=k(3^{1\over x})+c$ ,then the value of k is

(a)

log 3

(b)

-log 3

(c)

$-{1\over log3}$

(d)

${1\over log3}$

2. $\int sin^3 \ xdx$ is

(a)

${-3\over 4}cos \ x-{cos \ 3x\over 12}+c$

(b)

${3\over 4}cos \ x-{cos \ 3x\over 12}+c$

(c)

${-3\over 4}cos \ x+{cos \ 3x\over 12}+c$

(d)

${-3\over 4}sin \ x-{sin \ 3x\over 12}+c$

3. $\int {dx\over e^x-1}$is

(a)

$log|e^x|-log|e^x-1|+c$

(b)

$log|e^x|+log|e^x-1|+c$

(c)

$log|e^x-1|-log|e^x|+c$

(d)

$log|e^x+1|-log|e^x|+c$

4. $\int {sec^2x\over tan^2 \ x-1}$ dx

(a)

$2log|{1-tan x\over 1+tan \ x}|+c$

(b)

$log|{1+tan x\over 1-tan \ x}|+c$

(c)

${1\over2}log|{tan x+1\over tan \ x-1}|+c$

(d)

${1\over2}log|{tan x-1\over tan \ x+1}|+c$

5. $\int {1\over x\sqrt{(log \ x)^2+5}}dx$is

(a)

$log|x+\sqrt{x^2-5}|+c$

(b)

$log|logx+\sqrt{logx-5}|+c$

(c)

$log|logx+\sqrt{(logx)^2-5}|+c$

(d)

$log|logx-\sqrt{(logx)^2-5}|+c$

6. $\int { \frac { 1 }{ 2 } } { sec }^{ 2 }$ x dx is _____ + c.

(a)

$\frac { 1 }{ 2 }$ tan x

(b)

tan x

(c)

2 tan x

(d)

none of these

7. $\int { { 3 }^{ x+2 } }$ dx = __________+c.

(a)

$\frac { { 3 }^{ x } }{ log3 }$

(b)

$9\left( \frac { { 3 }^{ x } }{ log3 } \right)$

(c)

$\frac { { 3 }^{ x } }{ 9log3 }$

(d)

3x.9

8. $\int { \frac { \left( 1+logx \right) ^{ 2 } }{ x } }$ dx = _______+C.

(a)

$\frac { \left( 1+logx \right) ^{ 3 } }{ 3 }$

(b)

3 log ( 1 + log x)

(c)

2(1 + log x)

(d)

none of these

9. $\int { \frac { { e }^{ x } }{ \left( 1+{ e }^{ x } \right) ^{ 2 } } }$ dx =_______+c

(a)

$\frac { 1 }{ 1+{ e }^{ x } }$

(b)

-$\frac { 1 }{ 1+{ e }^{ x } }$

(c)

1 + ex

(d)

$\frac { \left( 1+{ e }^{ x } \right) ^{ 3 } }{ 3 }$

10. $\int { x }$ sin x dx = -x cos x + a, then a =

(a)

sin x + c

(b)

cos x + c

(c)

c

(d)

none of these

11. Part B

5 x 2 = 10
12. Integrate the following with respect to x.$\sqrt{x}$

13. Integrate the following with respect to x: ${1\over sin ^2 x}$

14. Integrate the following with respect to x:9xe3x

15. Evaluate $\int { \sqrt { x } -{ cos }^{ 2 } } \frac { x }{ 2 }$

16. Evaluate $\int { { x }^{ 2 } }$ log xdx

17. Part C

5 x 3 = 15
18. Integrate the following with respect to x:${x^{24}\over x^{25}}$

19. Integrate the following functions with respect to x:${1\over 6-4x}$

20. Evaluate : $\int (x-3)\sqrt{x+2}dx.$

21. Evaluate $\int { \frac { { sin }^{ 6 }x+cos^{ 6 }x }{ sin^{ 2 }xcos^{ 2 }x } }$

22. Evaluate $\int { \frac { 1 }{ { 4x }^{ 2 }-4x+3 } }$dx

23. Part D

3 x 5 = 15
24. Integrate the following with respect to x:$(1+x^2)^{-{1\over 2}}$

25. Evaluate $\int { \frac { dx }{ tanx+cotx+secx+cosecx } }$

26. Evaluate $\int { \frac { { e }^{ x }dx }{ { e }^{ 2x }+6{ e }^{ x }+5 } }$