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

int_0^(pi/2) sin x dx

int_0^(pi) sin3x dx=2/3

8) int_0^(2pi)cosx dx

int_(0)^(pi/4) sin^(3) x dx=(2)/(3)

int_0^(pi/2) (dx)/((4+9 cos^(2)x))

Prove that: int_0^(pi//2) cos^4 x dx =(3pi)/16

int_0^pi (cos^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 .

int_(0)^(pi//2) abs(sin(x-pi/4)) dx=