# Thread: Finding the volume of a solid using a double integral

1. ## Finding the volume of a solid using a double integral

Hi,I need help with the following;

Find the volume of the solid cut from the first octant by the surface z=4-x^2-y

I'm not sure how to set up the double integral. I'm also not sure even how to sketch this to determine the limits of integration. Are there steps I can follow to help sketch something like this?

Thanks

2. Originally Posted by s7b
Hi,I need help with the following;

Find the volume of the solid cut from the first octant by the surface z=4-x^2-y

I'm not sure how to set up the double integral. I'm also not sure even how to sketch this to determine the limits of integration. Are there steps I can follow to help sketch something like this?

Thanks
start by graphing it in each plain.

in the xy-plane, you have the curve $y = 4 - x^2$

in the xz-plane, you have the curve $z = 4 - x^2$

in the yz-plane, you have the curve $z = 4 - y$

with the aid of a little sketch using these traces, and perhaps some minor calculations if needed, we find that the volume is given by

$V = \int_0^2 \int_0^{4 - x^2} z~dy~dx$

where $z = 4 - x^2 - y$