Evaluate `int_0^(3/2) |xsin pix| dx`

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

Evaluate: int_-1^(3/2) |xsin(pix)|dx

Evaluate int_(-1)^((3)/(2))|xsin(pix)|dx

Evaluate int xsin^(2)x dx

Evaluate int xsin^(2)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 .

int_(0)^(1)|sin2pix|dx=

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

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