Find the volume of the region bounded by the cone and the paraboloid .
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I'm having a hard time even visualising the integration region. The following is my attempt to plot the paraboloid (in blue) and the cone (in brown) from x=-1..1 and y=-1..1.
Would I do this in rect-coords or cylindrical or what?
Thanks, but I have some questions:
How did you find their intersection? Did you solve the quartic polynomial:
?
Don't we need a triple integral here? Actually, I guess not since the integrand would be a constant "1" for volume. So you somehow used a double over R...
How did you determine that the integrand should be the difference between the surface functions, I.e. ?