Multiple Integral

**LL_5** · March 2nd 2009, 04:53 AM

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?

**Danny** · March 2nd 2009, 05:06 AM

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.

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