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The method we saw in
1.2 for evaluating
a double integral can be easily generalized here, together with Fubini's theorems. We will see some examples.
Compute the volume of the surface enclosed by the paraboloid whose equation is z
and the plane whose equation is z
The two surfaces intersect on a circle whose equations are
A cut paraboloid.
From this point, it will be easier to use polar coordinates. We get:
In fact this computation has been made using cylindrical coordinates (v.i. 2.5).