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 .

Find the value of int_(-1)^(2)|x sin pi x|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)abs(xsinpix)dx

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

Find the value of int (dx)/(1-2sinx) ​

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_-1^(2)f(x)dxdot

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_-1^(2)f(x)dxdot