Question

Let S be the solid bounded by the surface z = xy, the cylinders y = x^2 and y^2 = x and the plane z = 0. Find the volume.

Answer 1

This is nauseating :D
I haven't done this in a while, this involves double integrals, right?

Answer 2

yes :)

Answer 3

Well, then, it looks like you're integrating a function z = f(x,y) = xy
over a region. This SHOULD be easy, the tricky part is getting the region...

Answer 4

can you help me solving this?

Answer 5

Let's put that in maths language, shall we?
\[\huge \int\limits \int\limits xy \ dA\]Now all that remains is to find the region....

Answer 6

Now, the region is the cylinder formed by the bounded region of y = x^2 and x = y^2

Answer 7

And the plane z = 0, of course, but that's a mere formality :)
Let's take a look at the graphs of y = x^2 and x = y^2
WARNING I SUCK AT DRAWING

Answer 8

Say this is your xy plane

Answer 9

This is your y = x^2, a parabola :)