Show that `int_0^pixf(sinx)dx=pi/2int_0^pif(sinx)dxdot`

(i) Show that int_(0)^(pi)xf(sinx)dx =(pi)/(2)int_(0)^(pi)f (sin x)dx. (ii) Find the value of int_(-1)^(3//2)|x sin pix|dx .

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

If int_0^pi x f(sinx) dx=A int_0^(pi/2) f(sinx)dx , then A is (A) pi/2 (B) pi (C) 0 (D) 2pi

int_(0)^(2pi)|sinx|dx=?

int_0^pi tanx/(sinx+tanx)dx

int_(0)^(2pi)(sinx+cosx)dx=

Evaluate int_0^pi x^2 sinx dx

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Find int_0^(pi/2)dx/(1+sinx)

int_0^(pi/2) cosx/(1+sinx)dx