The value of \(\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx } \) is

(a)

\(\pi\)

(b)

\(2\pi\)

(c)

\(3\pi\)

(d)

\(4\pi\)

The value of \(\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx } \) is

(a)

\(\frac{1}{11000}\)

(b)

\(\frac{1}{10100}\)

(c)

\(\frac{1}{10010}\)

(d)

\(\frac{1}{10001}\)

The value of  \(\int _{ 0 }^{ \pi }{ { sin }^{ 4 }xdx } \) is

(a)

\(\frac{3\pi}{10}\)

(b)

\(\frac{3\pi}{8}\)

(c)

\(\frac{3\pi}{4}\)

(d)

\(\frac{3\pi}{2}\)

If \(\int _{ 0 }^{ a }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx=\frac { \pi }{ 8 } } \) then a is

(a)

4

(b)

1

(c)

3

(d)

2

\(\text { The value of } \int_{0}^{\frac{2}{3}} \frac{d x}{\sqrt{4-9 x^{2}}} \text { is }\)

(a)

\(\frac{\pi}{6}\)

(b)

\(\frac{\pi}{2}\)

(c)

\(\frac{\pi}{4}\)

(d)

\({\pi}\)

\(\int _{ 1 }^{ \sqrt { 3 } }{ \frac { dx }{ 1+{ x }^{ 2 } } } \) is __________

(a)

\(\frac { \pi }{ 3 } \)

(b)

\(\frac { \pi }{ 6 } \)

(c)

\(\frac { \pi }{ 12 } \)

(d)

\(-\frac { \pi }{ 6 } \)

The area bounded by the parabola y = x² and the line y = 2x is __________

(a)

\(\frac43\)

(b)

\(\frac23\)

(c)

\(\frac{51}{3}\)

(d)

\(\frac{30}{3}\)

The area enclosed by the curve y² = 4x, the x-axis and its latus rectum is ________ sq.units.

(a)

\(\frac23\)

(b)

\(\frac43\)

(c)

\(\frac83\)

(d)

\(\frac{16}{3}\)

The volume generated by the curve y² = 16x from x = 2 to x = 3 rotating about x - axis ......... cu. units

(a)

72π

(b)

\(\frac { 256\times 19 }{ 3 } \)ㅠ

(c)

40ㅠ

(d)

80ㅠ

 

\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x-cos \ x }{ 1+sin \ x cos \ x } dx= } \) ............

(a)

\(\frac { \pi }{ 2 } \)

(b)

0

(c)

\(\frac { \pi }{ 4 } \)

(d)

\( \pi\)