(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate

f(x,y)=y^{2}[itex]\sqrt{1-x^{2}}[/itex]

over the region

x^{2}+y^{2}< 1

2. Relevant equations

3. The attempt at a solution

using x limits between -1 & 1 followed by the y limits of 0 & [itex]\sqrt{1-x^{2}}[/itex]

[itex]\int[/itex][itex]\int[/itex]y^{2}[itex]\sqrt{1-x^{2}}[/itex].dy.dx

Evaluating this and multiplying be 2 to get the whole circle I get 0 as the 1 and -1 limits both give zero as the answer. Therefore I used the x limits of 0 & 1 and multiplied by 4 instead, this gave an answer of 4/9, however I have been given the answer of 32/45, and I have no idea how this could possibly be wrong.

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# Double integral circle limits

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