Question

Use a double integral in polar coordinates to find the volume of the solid bounded by the elliptical paraboloids z =x^2+y^2 and z=6-(x^2+2y^2)
please, help

Answer 1

@reemii

Answer 2

My question: how to find the polar coordinate of an ellipse? We know that if it is a circle, then polar coordinates are x = r cos t, y = r sint, how about ellipse?

Answer 3

in cylindrical

\(z = r^2\)
\(z = 6 - r^2\)

Answer 4

\(V = \int_V r dr d\theta dz\)

Answer 5

It is not cylindrical, the intersection of the surface is an ellipse, right?