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`

If f(x)=(sin x)/(x)AA x in(0,pi], prove that (pi)/(2)int_(0)^((pi)/(2))f(x)f((pi)/(2)-x)dx=int_(0)^( pi)f(x)dx

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

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

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

Write the value of int_0^(pi//2) (sinx) dx - int_0^(-pi//2) (cos x) dx

If f(x) is continuous in [0,pi] such that f(pi)=3 and int_0^(pi/2)(f(2x)+f^(primeprime)(2x))sin2x dx=7 then find f(0).

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

What is the value of int_0^pi((f(x))/(f(x)+f(pi/2-x)))dx ?

If int_(0)^(pi)xf(sinx)dx=A int_(0)^(pi//2) f(sinx)dx , then A is