## anonymous 4 years ago change to polar and then integrate

1. anonymous

$\int\limits_{0}^{2}\int\limits_{0}^{\sqrt{4-y ^{2}}} x ^{2}+y^{2} dxdy$

2. anonymous

i know it becomes $r^{2} r dr dTheta$

3. TuringTest

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

4. anonymous

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

5. TuringTest

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

6. anonymous

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

7. anonymous

8. TuringTest

yes

9. TuringTest

and what are the bounds on theta?

10. anonymous

0 to 2pi

11. 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...?

12. anonymous

0 to pi

13. TuringTest

yes

14. anonymous

so would i ge 4 pi

15. TuringTest

yes

16. anonymous

ur a life saver

17. TuringTest

no problem, happy to help