The value of \(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ \left( \frac { { 2x }^{ 7 }-{ 3x }^{ 5 }+{ 7x }^{ 3 }-x+1 }{ { cos }^{ 2 }x } \right) dx } \) is 

(a)

4

(b)

3

(c)

2

(d)

0

The area between y² = 4x and its latus rectum is

(a)

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

(b)

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

(c)

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

(d)

\(\frac{5}{3}\)

The value of \(\int _{ 0 }^{ \pi }{ \frac { dx }{ 1+{ 5 }^{ cos\ x } } } \) is

(a)

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

(b)

\(\pi\)

(c)

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

(d)

\(2\pi\)

The value of \(\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3x\ dx }\ is\)

(a)

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

(b)

\(\frac{2}{9}\)

(c)

\(\frac{1}{9}\)

(d)

\(\frac{1}{3}\)

The value of \(\int _{ 0 }^{ \infty }{ { e }^{ -3x }{ x }^{ 2 }dx } \) is

(a)

\(\frac{7}{27}\)

(b)

\(\frac{5}{27}\)

(c)

\(\frac{4}{27}\)

(d)

\(\frac{2}{27}\)