Can someone help me please

Thanx

Edgar

a)Evaluate the integral

integral from minus infintiy to infinity of 1/(1+x)^4 dx

b)Where are the poles of 1/(1+z)^4 ?

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- Dec 1st 2006, 05:41 AMedgar davidsIntegration and complex nos
Can someone help me please

Thanx

Edgar

a)Evaluate the integral

integral from minus infintiy to infinity of 1/(1+x)^4 dx

b)Where are the poles of 1/(1+z)^4 ? - Dec 1st 2006, 09:38 AMThePerfectHacker
You need to find,

$\displaystyle \int_{\infty}^{\infty} \frac{1}{(1+x)^4}dx$

The function has a vertical asymptote at $\displaystyle x=-1$

Thus you need to do,

$\displaystyle \int_{-\infty}^{-1^-} \frac{1}{(1+x)^4} dx+\int_{-1^+}^{\infty} \frac{1}{(1+x)^4} dx$

Which is,

$\displaystyle (-1/5)(1+x)^{-5}|_{-\infty}^{-1^-}+(-1/5)(1+x)^{-5}|_{-1^+}^{\infty}$

That looks unbounded to me.

Quote:

b)Where are the poles of 1/(1+z)^4 ?