#### Integral Calculus – I Book Back Questions

12th Standard EM

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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. $\frac { 1 }{ { x }^{ 3 } }$dx is

(a)

$\frac { -3 }{ { x }^{ 2 } } +c$

(b)

$\frac { -1 }{ 2{ x }^{ 2 } } +c$

(c)

$\frac { -1 }{ { 3x }^{ 2 } } +c$

(d)

$\frac { -2 }{ { x }^{ 2 } } +c$

2. $\frac{logx}{x}$dx , x > 0 is

(a)

$\frac12$(log x)2 + c

(b)

-$\frac12$(log x)2

(c)

$\frac { 2 }{ { x }^{ 2 } } +c$

(d)

$\frac { 2 }{ { x }^{ 2 } } +c$

3. $\left[ \frac { 9 }{ x-3 } -\frac { 1 }{ x+1 } \right]$dx is

(a)

$log\left| x-3 \right|-log \left| x+1 \right| +c$

(b)

$log\left| x-3 \right|+log \left| x+1 \right| +c$

(c)

$9log\left| x-3 \right|-log \left| x+1 \right| +c$

(d)

$9log\left| x-3 \right|+log \left| x+1 \right| +c$

4. $\int _{ 0 }^{ 1 }{ (2x+1) } dx$ is

(a)

1

(b)

2

(c)

3

(d)

4

5. $\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } }$ dx is

(a)

1

(b)

2$\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } }$dx

(c)

0

(d)

${ e }^{ { x }^{ 4 } }$

6. 3 x 2 = 6
7.  Integrate the following with respect to x.

$\frac { 1 }{ \sqrt { x+1 } +\sqrt { x-1 } }$

8. Integrate the following with respect to x.
ex log a + ea log a − enlog x

9. Integrate the following with respect to x.
$\sqrt { 1-sin2x }$

10. 3 x 3 = 9
11. Evaluate $\int { \frac { { 5+5e }^{ 2x } }{ { e }^{ x }+{ e }^{ -x } } dx }$

12. Evaluate $\int _{ -1 }^{ 1 }{ ({ x }^{ 2 }+x)dx }$

13. Evaluate the integral as the limit of a sum: $\int _{ 1 }^{ 2 }{ { x }^{ 2 } }$ dx

14. 2 x 5 = 10
15. Evaluate $\int { { sin }^{ 2 }xdx }$

16. Evaluate
$\int _{ 0 }^{ \infty }{ { e }^{ -2x }{ x }^{ 5 }dx }$