- #1

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## Main Question or Discussion Point

Evaluate the following integral using the residue theorem:

Any hint?

Any hint?

- Thread starter asmani
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- #1

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Evaluate the following integral using the residue theorem:

Any hint?

Any hint?

- #2

lurflurf

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and

(n+1)u

with u=e

(n+1)e

- #3

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Sorry, I can't see how to use these facts. Can you give any further hint, please?

Besides, what contour should be chosen?

Thanks

Besides, what contour should be chosen?

Thanks

Last edited:

- #4

lurflurf

Homework Helper

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let

z=e

dx=dz/(i z)

sin(x)=((z-1/z)/(2i))

sin

[tex]\int_0^\pi \sin^{2n}(x) dx=\frac{1}{2}\int_{-\pi}^\pi \sin^{2n}(x) dx=\oint_{|z|=1}\left( \frac{z-\frac{1}{z}}{2i}\right)^{2n}\frac{dz}{2i z}[/tex]

- #5

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Thanks!

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