`int_- 1^(3/2)|xsin(pix)|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_(-1)^(3/(2))|x"sin"(pix)|dx

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

int_(-2)^(2)|xcos pix|dx is equal to

Evaluate sum_(n=1)^(1000)int_(n-1)^(n)|cos2pix|dx

Evaluate sum_(n=1)^(1000)int_(n-1)^(n)|cos2pix|dx

Prove that following: underset(-1)overset(3//2)int|xsin pi x| dx