Evaluate: `int_0^(3//2) |x sin pi x| dx`.

Evaluate int_(0)^((3)/(2))|x sin pi x|dx

Evaluate :int_(0)^((3)/(2))|x sin pi x|dx

(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 .

Evaluate int_0^(-pi//2) sin x dx

Evaluate int_(0)^(pi/2) x sin x dx .

Evaluate int_0^(pi/2) sin^2x dx

Evaluate int_0^(pi/2) sin^7x dx

Evaluate : int_0^(pi/2) log sin x dx .

int_0^(pi/2) sin x sin 2x dx

int_0^(pi//2) sin^3 x dx