Prove that `int0 1sin^(-1)x""dx=pi/2-1`

int_0^1 sin^-1 x dx=pi/2-1

int_0^1 sin^-1x dx=pi/2-1

Prove that int_(0)^(1)sin^(-1)xdx=(pi)/(2)-1

Prove that int_(0)^(tan^(-1)x)/x dx=1/2int_(0)^((pi)/2)x/(sinx)dx .

int_(0)^(1) sin^(-1) x dx =(pi)/(2) -1

Prove that int_0^1 tan^-1((2x-1)/(1+x-x^2))dx=0

Prove that int_0^a f(x)dx=int_0^af(a-x)dx , hence evaluate int_0^pi(x sin x)/(1+cos^2 x)dx

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

Prove that :int_(0)^((pi)/(2))sqrt(1-sin2x)dx=2(sqrt(2)-1)

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 .