For the double integral shown below, investigate values of k that make the integral converge. $\displaystyle \int\int_{(x^2)+(y^2)<=1} \frac{dA} {(x^2+y^2)^k}$ To what value does it converge?
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Originally Posted by LL_5 For the double integral shown below, investigate values of k that make the integral converge. $\displaystyle \int\int_{(x^2)+(y^2)<=1} \frac{dA} {(x^2+y^2)^k}$ To what value does it converge? Switch to polar coords $\displaystyle \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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