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evaluate [tex]\int \int \int _E \sqrt{x^2+y^2} dV[/tex], where E is the solid bounded by the circular parabola [tex]z=9-4(x^2+y^2) [/tex] and the xy-plane

so here's what I did, i tried to set this up in cylindrical coordinates.

is when [tex]z=9-4(x^2+y^2)[/tex] equals with the xy-plane

so this means that z=0 and x=y

[tex]0=9-4(2x^2)[/tex]

[tex]r=\frac{3}{\sqrt{8}}[/tex]

[tex]z=9-4r^2[/tex]

theta should rotate in a ciricle so it should be 2 pi

[tex]\int_0 ^{2 \pi} \int_0 ^{\frac{3}{\sqrt{8}}}\int _0 ^ {9-4r^2} r rdzdrd \theta [/tex]

i evaluated this twice but it seems not to be the answer, where did I go wrong?

so here's what I did, i tried to set this up in cylindrical coordinates.

**the radius:**is when [tex]z=9-4(x^2+y^2)[/tex] equals with the xy-plane

so this means that z=0 and x=y

[tex]0=9-4(2x^2)[/tex]

[tex]r=\frac{3}{\sqrt{8}}[/tex]

**the z-height:**[tex]z=9-4r^2[/tex]

**the angle:**theta should rotate in a ciricle so it should be 2 pi

**the setup:**[tex]\int_0 ^{2 \pi} \int_0 ^{\frac{3}{\sqrt{8}}}\int _0 ^ {9-4r^2} r rdzdrd \theta [/tex]

i evaluated this twice but it seems not to be the answer, where did I go wrong?

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