Question

Find the exact volume of the solid between the paraboloids z=2x^2+y^2 and z=8−x^2−2y^2 and inside the cylinder x^2+y^2=1

Answer 1

I really don't know how to set this up. Would it be something like ∫∫(2x^2+y^2)-(8-x^2-2y^2)dA + ∫∫(x^2+y^2-1)dA ?

If so, how would I find the bounds of integration?

Answer 2

int tita=0-2pi r=0-1 z=r2-8-r2

Answer 3

What are you doing? Not sure I understand.

Answer 4

rdzdrdtita
=8r-2r3 dr=4r2-1/2r4]0-1=3.5
3.5(2pi)=7pi

Answer 5

I don't understand

Answer 6

unfortunetly my bamboo not work properly to show you.
but I calculated triple integral.

Answer 7

How? How would you do this with a double integral?