cal 2

**lay137** · February 1st 2007, 06:26 PM

evaluate the limits of pie and 0 (x+sinnx)dx

**ThePerfectHacker** · February 1st 2007, 07:17 PM

Originally Posted by lay137

evaluate the limits of pie and 0 (x+sinnx)dx

What are you trying to find? The Fourier Series?

We need to find, (assume $n>1$ )
$\int_0^{\pi} (x+\sin nx )dx$
By linearity,
$\frac{1}{2}x^2-\frac{1}{n}\cos nx\big|^{\pi}_0$
$\frac{1}{2}\pi^2-\frac{1}{n}\cos \pi n+\frac{1}{2}$
If $n$ is even, then we have,
$\frac{1}{2}\pi^2 - \frac{1}{2}+\frac{1}{2}=\frac{1}{2}\pi^2$ .
If $n$ is odd, then we have,
$\frac{1}{2}\pi^2+\frac{1}{2}+\frac{1}{2}=\frac{1}{ 2}\pi^2+1$

**topsquark** · February 2nd 2007, 04:21 AM

Originally Posted by lay137

evaluate the limits of pie and 0 (x+sinnx)dx

And, just as a note, the Greek letter $\pi$ is "pi", not "pie!"

-Dan

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