Determine a positive integer `n` such that `int_0^(pi/2)x^nsinx dx=3/4(pi^2-8)`

Determine a positive integer n such that (pi)/(2)x^(n)sin xdx=(3)/(4)(pi^(2)-8)

8) int_0^(2pi)cosx dx

The value of n for which int_(0)^(pi//2)x^(n)sinxdx=(3)/(4)(pi^(2)-8) is

int_0^(pi/8) tan^(2) (2x) dx =

If n is a positive integer, prove that: int_0^(2pi) (cos(n-1)x-cosnx)/(1-cosx)dx=2pi , hence or otherwise, show that int_0^(2pi) (sin((nx)/2)/sin(x/2))^2dx=2npi .

If n is a positive integer, prove that: int_0^(2pi) (cos(n-1)x-cosnx)/(1-cosx)dx=2pi , hence or otherwise, show that int_0^(2pi) (sin((nx)/2)/sin(x/2))^2dx=2npi .

int_0^(2pi) e^(x/2) sin (x/2+pi/4) dx =

For a positive integer n, let I _(n) int _(-pi)^(pi) ((pi)/(2) -|x|) cos nx dx Find the value of [I _(1) + I _(3) +I_(4)] where [.] denotes greatest integer function.

For a positive integer n, let I _(n) =int _(-pi)^(pi) ((pi)/(2) -|x|) cos nx dx Find the value of [I _(1) + I _(3) +I_(4)] (where [.] denotes greatest integer function) .

For a positive integer n, let I _(n) =int _(-pi)^(pi) ((pi)/(2) -|x|) cos nx dx Find the value of [I _(1) + I _(3) +I_(4)] (where [.] denotes greatest integer function) .