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

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

Evaluate :int_(0)^((3)/(2))|x cos 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) x/(sinx+cos x)dx .

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

Evaluate: int_0^(pi//4)sin3xsin2x\ dx

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

Evaluate: int_(-pi//2)^(pi//2)xsin dx