The value of \(\int _{ -\frac{\pi}{2}}^{ \frac{\pi}{2}}\) cos x dx is _______.

(a)

0

(b)

2

(c)

1

(d)

4

The value of \(\int _{ 2 }^{ 3 }{ f(5-x) } dx-\int _{ 2 }^{ 3 }{ f(x) } dx\) is _______.

(a)

1

(b)

0

(c)

-1

(d)

5

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function \(\Gamma \)(n) when n = 8 _______.

(a)

5040

(b)

5400

(c)

4500

(d)

5540

If n > 0, then \(\Gamma \)(n) is _______.

(a)

\(\int _{ 0 }^{ 1 }{ { e }^{ -x }x^{ n-1 } } \) dx

(b)

\(\int _{ 0 }^{ 1 }{ { e }^{ -x }{ x }^{ n } } dx\)

(c)

\(\int _{ 0 }^{ \infty }{ { e }^{ x }{ x }^{ -n } } \ dx\) 

(d)

\(\int _{ 0 }^{ \infty }{ { e }^{ -x }{ x }^{ n-1 } } \ dx\)

\(\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } } \)dx is _______.

(a)

12

(b)

4

(c)

4!

(d)

64