Double Integral Help!

**aeubz** · October 18th 2008, 02:29 PM

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.

**aeubz** · October 18th 2008, 02:35 PM

oops forgot to upload the image

**mr fantastic** · October 18th 2008, 03:17 PM

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 ....

**11rdc11** · October 18th 2008, 03:38 PM

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

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

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

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

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