psk981
change to polar and then integrate



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psk981
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\[\int\limits_{0}^{2}\int\limits_{0}^{\sqrt{4y ^{2}}} x ^{2}+y^{2} dxdy\]

psk981
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i know it becomes \[r^{2} r dr dTheta\]

TuringTest
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yes, which simplifies to\[r^3drd\theta\]where are you stuck?

psk981
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the sqrt term becomes x^2+y^2= 4 right

TuringTest
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x^2+y^2=r^2
what is the radius of the circle in question?

psk981
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so i should get r^4/4 evaluated from 0 to 2
then i should get 4 dtheta

psk981
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radius should be 2

TuringTest
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yes

TuringTest
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and what are the bounds on theta?

psk981
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0 to 2pi

TuringTest
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remember that sqrt(4y^2) is only the *top* of the circle, the bottom would require a negative sign, so the bounds on theta are only...?

psk981
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0 to pi

TuringTest
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yes

psk981
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so would i ge 4 pi

TuringTest
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yes

psk981
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ur a life saver

TuringTest
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no problem, happy to help