Question

Need some help evaluating an integral...

Answer 1

\[\int\int_E\int\sqrt{3x^2+3z^2}dV\] where E is the solid bounded by \(y=2x^2+2z^2\) and the plane \(y=8\)

Answer 2

not sure how to do the triple int notation in \(\LaTeX\) but you know what i mean

Answer 3

\[\large \iiint \limits_{E} \sqrt{3x^2+3z^2}dV\]

Answer 4

indeed, thanks

Answer 5

x^2+z^2 should hint you to switch to spherical/cylindrical

Answer 6

So, would I be correct in saying that the limits would be
\[2x^2+2z^2\le y\le8 \\ 0\le r\le2 \\ 0\le \theta\le 2\pi\]
?
if that's accurate I know what im doing lol

Answer 7

thats right !
the projection in xz plane is a disk of radius 2

Answer 8

kay, i've got it from here.. the setup was causing me some issues lol.. thanks