anonymous
  • anonymous
change to polar and then integrate
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{0}^{2}\int\limits_{0}^{\sqrt{4-y ^{2}}} x ^{2}+y^{2} dxdy\]
anonymous
  • anonymous
i know it becomes \[r^{2} r dr dTheta\]
TuringTest
  • TuringTest
yes, which simplifies to\[r^3drd\theta\]where are you stuck?

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anonymous
  • anonymous
the sqrt term becomes x^2+y^2= 4 right
TuringTest
  • TuringTest
x^2+y^2=r^2 what is the radius of the circle in question?
anonymous
  • anonymous
so i should get r^4/4 evaluated from 0 to 2 then i should get 4 dtheta
anonymous
  • anonymous
radius should be 2
TuringTest
  • TuringTest
yes
TuringTest
  • TuringTest
and what are the bounds on theta?
anonymous
  • anonymous
0 to 2pi
TuringTest
  • TuringTest
remember that sqrt(4-y^2) is only the *top* of the circle, the bottom would require a negative sign, so the bounds on theta are only...?
anonymous
  • anonymous
0 to pi
TuringTest
  • TuringTest
yes
anonymous
  • anonymous
so would i ge 4 pi
TuringTest
  • TuringTest
yes
anonymous
  • anonymous
ur a life saver
TuringTest
  • TuringTest
no problem, happy to help

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