1. ## another triple integration!

Use a triple integral to find the volume of the solid bounded by the surface y=x^2 and the planes y+z=4 and z=0.

Thank you very much.

2. Try this:

$2\int_{0}^{2}\int_{x^{2}}^{4}\int_{0}^{4-y}dzdydx$

Here's a haphazard attempt at a graph of your region. I hope it gives you some idea of what it looks like.

3. Hi galactus,

Thank you very much.

Why is the integration of dy from x^2 to 4 ?

4. Hello kittykat:

Because that's where the plane 'slices' the parabola x^2.

Here's a graph. The line y=4 is where the plane z=4-y meets the parabola.

So, you integrate over y from x^2 to 4. See?.

At x=2, y=x^2=4

The 3-D I posted is rather cock-eyed, but you can see it there.

I gonna go mow grass now, so I may not be back for a few hours.

5. " I gonna go mow grass now, so I may not be back for a few hours. "

Enjoy the green and beautiful grass!

6. Actually, it's rather hot here in PA today.

Did you follow what I attempted to explain?.

7. Not really, I am still thinking ....

I am very bad in visualize the 3D objects. Thus , it is so how difficult for me to set up the integrals for triple integration.

Thanks! I got it now!

8. First, try drawing your parabola y=x^2. That's easy enough. It's the plane rising up the z-axis that's the booger to visualize. Try plotting various points for it.

z=4-y, if y=0, z=4

If y=4, z=0. See there?. That's where the plane intersects the parabola in the xy plane.

Then it rises up the z-axis at a slant and intersects the z axis at y=0.