Purchase Solution

Evaluating an Integral With a 2nd Order Pole using the Residue Theorem

Not what you're looking for?

Ask Custom Question

Evaluate the integral from 0 to INF of:

(x^a)/(x^2 +4)^2 dx, -1 < a < 3

We are to use f(z)= (z^a)/(z^2 +4)^2,
with z^a = e^(a Log z), Log z= ln|z| + i Arg z, and
-pi/2 < Arg z < 3pi/2.

I have found the residue at 2i to be:
[2^a(1-a)/16]*[cos ((pi*a)/2) + i sin ((pi*a)/2).

Please let me know if this is correct and how to solve this problem.

Many thanks for your help.

Purchase this Solution

Solution Summary

The residue theorem is used to evaluate an integral. The solution is well presented and includes a diagram.

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.