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#### Integral Calculus – I Two Marks Questions

12th Standard EM

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Integrate the following with respect to x.

$\frac { 8x+13 }{ \sqrt { 4x+7 } }$

2.  Integrate the following with respect to x.

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

3. Integrate the following with respect to x.
$\frac { { x }^{ 3 } }{ x+2 }$

4.  Integrate the following with respect to x.
$If\quad f' \prime x=\frac { 1 }{ x } andf(1)=\frac { \pi }{ 4 } ,\quad then\quad findf(x)$

5. Integrate the following with respect to x.
$\frac { { e }^{ 3x }+{ e }^{ 5x } }{ { e }^{ x }+{ e }^{ -x } }$

6. If f ' (x) = ex and f (0)= 2, then find f (x)

7. Integrate the following with respect to x.
$\frac { 1 }{ { sin }^{ 2 }x{ cos }^{ 2 }x } [Hint:si{ n }^{ 2 }+{ cos }^{ 2 }x=1]\quad$

8. Integrate the following with respect to x.
$\frac { { e }^{ 3logx } }{ { x }^{ 4 }+1 }$

9. Evaluate the following integrals:
$\frac { dx }{ { { 2-3x-2x }^{ 2 } } }$

10. Evaluate the following integrals:
ഽ log(x −$\sqrt { { x }^{ 2 }-1 }$) dx

11. Evaluate the following
$\int _{ 0 }^{ \infty }{ { e }^{ -4x } } { x }^{ 4 }dx$

12. Evaluate $\int { { a }^{ 3{ log }_{ a }x } } dx$

13. Evaluate $\int { \frac { { 2 }^{ x }+{ 3 }^{ x } }{ { 5 }^{ x } } dx }$

14. If f'(x) = 8x3 -2x2, f(2) = 1, find f(x)

15. If $\int _{ 0 }^{ a }{ { 3x }^{ 2 } } dx=8$ find the value of a