hi just confused on this integration.

$\displaystyle

\int xcosx

$

how would i go about solving?

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- Nov 1st 2008, 09:56 PMjvignaciointegrate problem
hi just confused on this integration.

$\displaystyle

\int xcosx

$

how would i go about solving? - Nov 1st 2008, 10:00 PMmr fantastic
There are many techniques. One such is integration by parts. You'll find it done as an example somewhere in here: http://en.wikipedia.org/wiki/Integra...#More_examples.

- Nov 1st 2008, 10:10 PMjvignacio
- Nov 1st 2008, 10:13 PMmr fantastic
- Nov 1st 2008, 10:21 PMjvignacio
- Nov 1st 2008, 10:30 PMmr fantastic
$\displaystyle \frac{dy}{dx} = \sin x + x \cos x$

Integrate both sides with respect to x:

$\displaystyle y = \int \sin x + x \cos x \, dx = \int \sin x \, dx + \int x \cos x \, dx = - \cos x + \int x \cos x \, dx$

Substitute $\displaystyle y = x \sin x$:

$\displaystyle x \sin x = - \cos x + \int x \cos x \, dx$

Now re-arrange to make $\displaystyle \int x \cos x \, dx$ the subject and add a "+ C".

**Next time post the whole question - as you can now see the first part was essential to answering the second part.**