Mathematics

Mathematics

Problem

The region in the first quadrant bounded by

y=x^{2}

and the

x

–axis from

x=0

to

x=2

serves as the common base for two solids. • Solid

M

has cross sections perpendicular to the

x

–axis that are squares. • Solid

N

has cross sections perpendicular to the

y

–axis that are squares. Find the exact difference

V_{N}-V_{M}

between the volumes of the two solids.

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