Find the value of the following: `int_0^pi (sin^2(x/2)-cos^2(x/2))dx`

If the value of int_0^pi(x/(1+sinx))^2dx=lambda , then find the value of the integral =int_0^pi[(2x^2*cos^2(x/2))/(1+sinx)^2]dx

Evaluate the following : int_(0)^(pi//2)x sin x dx

Evaluate the following integral: int_0^(pi//2)(cos^2x)/(1+3sin^2x)dx

Evaluate the following integral: int_0^(pi//2)|sin x-cos x|dx

Evaluate the following integral: int_0^(pi//2)x^2cos2x\ dx

Evaluate the following integral: int_0^(pi//2)(sin^2x)/((1+cos x)^2)dx

Evaluate the following integral: int_0^(pi//2)(cos x)/(1+sin^2x)dx

Evaluate the following integral: int_0^(pi//2)(cos x)/(1+sin^2x)dx

Evaluate the following integral: int_0^(pi//2)1/(a^2sin^2x+b^2cos^2x)dx

Evaluate the following : int_(0)^(pi//4)(sin 2x)/(sin^(4)x+cos^(4)x)dx.