Find the value of `int_(-1)^(3/2)|xsinpix|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)|xsinpix|dx

Find the value of int_(0)^(1)x^(2)dx

Find the value of int(1)/(2x-3)dx

Evaluate int_(-1)^((3)/(2))|x sin(pi x)|dx

If [:] denotes the greatest integer function, then find the value of int_(1)^(2)[3x]dx

Find the value of int_(0)^(1)x(1-x)^(n)dx

Evaluate: int_(-1)^(4)f(x)dx=4 and int_(2)^(4)(3-f(x))dx=7 then find the value of int_(2)^(-1)f(x)dx

The value of int_(-2)^(3)|1-x^(2)|dx