Thread: Find the volume bounded by the paraboloid.

Find the volume bounded by the paraboloid z=x^2 + y^2 +6 and the planes x=0, y=0, z=0, x+y=2. Would I be integrating this? I have no clue how to tackle this problem. I have looked through my textbook, searched through my personal notes, and even searched through the notes my professor uploads online for his students to use. I would like to learn how to do this type of problem, step by step, so I can figure out the answer. I greatly appreciate the help. Peace! Thank you.

It would help if you started by drawing a rough sketch of the region to be integrated. It should be clear that since it's bounded by x = 0, y = 0 and z = 0, that the region is only in the first octant. Then it will be bounded above by the paraboloid z = x^2 + y^2 + 6 (why would it be bounded above btw?) and bounded on the right by x + y = 2.

Can you come up with a triple integral from that?

I just don't understand it. Is it possible to show me an example of a problem similar to this one? I have had no luck in finding one.

Thank you.