Hello people! I need help to evaluate the integral on the following attachment. The problem is number 5. An explanation will be much appreciated too.
$\displaystyle \int_0^\pi \int_0^x x\sin{y}~dydx$
$\displaystyle \int_0^\pi -x\cos{y}\bigg|^x_0~dx$
$\displaystyle \int_0^\pi -x\cos{x} + x\cos{0}~dx$
$\displaystyle \int_0^\pi (-x\cos{x} +x)~dx$
Next you going to need to use IBP
$\displaystyle \int^\pi_0 -x\cos{x}dx +\int^\pi_0 xdx$
$\displaystyle -[x\sin{x} - \int^\pi_0 \sin{x}dx] +\frac{x^2}{2}$
$\displaystyle -x\sin{x} - \cos{x} +\frac{x^2}{2}\bigg|^\pi_0$