# Thread: Integrate with respect to x and y with a volume

1. ## Integrate with respect to x and y with a volume

Let S be the surface defined by $z= f(x,y) = 1 - y - x^2$
Let V be the volume of the 3-D region in the first octant bounded by S and the coordinate planes.

Setup the iterated integrals for V in two ways:

a) integrate first respect to x and then respect to y
b) integrate first respect to y and then respect to x

I dont know how to do this problem. I am completely lost.
Thank you

2. ## Re: Integrate with respect to x and y with a volume

This is a pretty standard Calculus problem. If you were given it as home work you should have been given some instruction.

One of the "coordinate plane boundaries" is z= 0. $z= 1- y- x^2= 0$ on the curve $y= 1- x^2$ which goes from (0, 1) to (1, 0).
So take x from 0 to 1 and, for each x, y from 0 to $1- x^2$. And of course z goes from 0 up to $1- x^2$.

3. ## Re: Integrate with respect to x and y with a volume

You left me scratching my head more than the problem itself.
Im more confused than when i first started.

Oh, i think its an iterated integral. So a triple integral. This is something we cover next week. I think i am a head of my self.