Question

How do I set up this integral, under the surface z= 1+x^2y^2 and above the region enclosed by x = y^2 and x = 4.

Answer 1

\[z=1+x^2y^2\] basically this part :P

Answer 2

Or is their a way to do this, without having to draw it out?

Answer 3

@ganeshie8

Answer 4

you want to setup the volume integral is it ?

Answer 5

Yup

Answer 6

try this
\[\int\limits_{-2}^2~~\int\limits_{y^2}^4~\int\limits_{0}^{1+x^2y^2}~1 ~dzdxdy\]

Answer 7

How did you get the -2 to 2 ?

Answer 8

solve x=y^2 and x=4
before even doing that, sketch the curves in xy plane maybe..

Answer 9

The integral IS \[\int\limits_{-2}^{2}\int\limits_{y^2}^{4} (1+x^2y^2)dxdy\] but I don't know how to get the -2 to 2 limits

Answer 10

sketch below curves in xy plane
x = y^2
x = 4

Answer 11

That's it haha?

Answer 12

after sketching if it becomes obvious, then yes thats it :)

Answer 13

Oh I see, my problem was I was sketching y=x^2 xDDDD

Answer 14

Thanks!! :D

Answer 15

if you want it more challenging, you may try setting up `dydx` instead of `dxdy` :P

Answer 16

Loool I'll try that for fun