Show that `int_(0)^(1)(cos^(-1)x)^(2)dx=pi-2`.

int_(0)^(1)cos^(-1)x dx

Show that : int_(1)^(2)sqrt((x-1)(2-x))dx=(pi)/(8) .

int_(0)^(a)cos^(-1).(1-x^(2))/(1+x^(2))dx

Show that, int_(0)^(pi)xf(sinx)dx=(pi)/(2)int_(0)^(pi)f(sinx)dx .

Prove that, int_(0)^(2pi)(cosx)/(1+sin^(2)x)dx=0

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

The value of int_(0)^(1)cos^(-1)(x-x^(2))-sqrt((1-x^(2))(2x-x^(2)))dx is equal to ___________.

Show that, int_(0)^((pi)/(2))f(sin2x)sinxdx=sqrt(2)int_(0)^((pi)/(4))f(cos2x)cosxdx

Prove that, int_(0)^((pi)/(2))cos^(n)x cos nx dx=(pi)/(2^(n+1)) .

Show that, int_(0)^((pi)/(2))(sin2x dx)/(sin^(4)x+cos^(4)x)=(pi)/(2)