# Multiple Integral

• March 2nd 2009, 04:53 AM
LL_5
Multiple Integral
For the double integral shown below, investigate values of k that make the integral converge.

$\int\int_{(x^2)+(y^2)<=1} \frac{dA} {(x^2+y^2)^k}$

To what value does it converge?
• March 2nd 2009, 05:06 AM
Jester
Quote:

Originally Posted by LL_5
For the double integral shown below, investigate values of k that make the integral converge.

$\int\int_{(x^2)+(y^2)<=1} \frac{dA} {(x^2+y^2)^k}$

To what value does it converge?

Switch to polar coords

$\int_0^{2 \pi} \int_0^1 r^{1-k} dr d \theta = 2\pi \int_0^1 r^{1-k} dr$ and determine the k values that there's an answer.