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

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

loser66 · Answer

@reemii

loser66 · Answer

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?

irishboy123 · Answer

in cylindrical

$z = r^2$
$z = 6 - r^2$

irishboy123 · Answer

$V = \int_V r dr d\theta dz$

loser66 · Answer

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

irishboy123 · Answer

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