# Math Help - Double Integral Help!

1. ## Double Integral Help!

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.

2. oops forgot to upload the image

3. Originally Posted by aeubz
oops forgot to upload the image
The integral with respect to y of x sin y is just -x cos y. x is treated like a constant ....

4. Originally Posted by mr fantastic
The integral with respect to y of x sin y is just -x cos y. x is treated like a constant ....
$\int_0^\pi \int_0^x x\sin{y}~dydx$

$\int_0^\pi -x\cos{y}\bigg|^x_0~dx$

$\int_0^\pi -x\cos{x} + x\cos{0}~dx$

$\int_0^\pi (-x\cos{x} +x)~dx$

Next you going to need to use IBP

$\int^\pi_0 -x\cos{x}dx +\int^\pi_0 xdx$

$-[x\sin{x} - \int^\pi_0 \sin{x}dx] +\frac{x^2}{2}$

$-x\sin{x} - \cos{x} +\frac{x^2}{2}\bigg|^\pi_0$