91Ó°ÊÓ

Compute \(\int_{0}^{\sqrt{2} / 2} \int_{-\sqrt{1-2 x^{2}}}^{\sqrt{1-2 x^{2}}} x d y d x\)

Find the volume bounded by \(4 x^{2}+y^{2}=4 z\) and \(z=2\).

A swimming pool is circular with a 40 meter diameter. The depth is constant along east-west lines and increases linearly from 2 meters at the south end to 7 meters at the north end. Find the volume of the pool.

What are the parallels between Fubini's Theorem and Clairaut's Theorem?