If `f(x)=(sinx)/xAAx in (0,pi],` prove that `pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx`

int_0^(pi/2) (sinx)/(1+Cos^2x)dx

int_(0)^( pi)xf(sin x)dx=(pi)/(2)int_(0)^( pi)f(sin x)dx

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

prove that : int_(0)^(2a) f(x)dx = int_(0)^(a) f(x)dx + int_(0)^(a)f(2a-x)dx

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

If f(x) is continuous in [0,pi] such that f(pi)=3 and int_(0)^((pi)/(2))(f(2x)+f'(2x))sin2xdx=7 then find f(0)

Evaluate: int_0^(pi//2)x/(sinx+cosx)dx

Prove the equality int_(0)^(pi) f (sin x) dx = 2 int_(0)^(pi//2) f (sin x) dx