# Thread: Finding volume using a double integral?

1. ## Finding volume using a double integral?

Here is the question...

Fine exactly the volume under the surface $\displaystyle z=(1-x^2)(1-y^2)$ in the first octant.

Can someone solve this and explain to me how to do it? The main thing I am confused about is how to find the limits. I know I am supposed to use the fact that it is in the first octant to find the limits, but I am not sure what to do with that information. Thanks in advance.

2. Originally Posted by Infernorage
Here is the question...

Fine exactly the volume under the surface $\displaystyle z=(1-x^2)(1-y^2)$ in the first octant.

Can someone solve this and explain to me how to do it? The main thing I am confused about is how to find the limits. I know I am supposed to use the fact that it is in the first octant to find the limits, but I am not sure what to do with that information. Thanks in advance.
What you need to know is when does the surface intersect the xy- plane in the first octant?

Here is a hint to get you started.

To find out set $\displaystyle z=0$ (why?)

And solve

$\displaystyle 0=(1-x^2)(1-y^2)$ for the values of x and y.

Just use the zero product rule.

Now sketch the region over you need to integrate. It turns out very nice.