Math $156$

Homework $3-$ Volumes $\backslash$#$1$

Due: Tuesday, February $4,2025$ in Crowdmark

For each of the problems, do all of the following:

$-$ sketch all curves, determine the region in question;

$-$ find and label appropriate intersection points;

$-$ draw a typical approximating rectangle,

$-$ sketch a typical disk$/$washer or cylindrical shell,

$-$ set up your integral.

Let $\backslash (\backslash$mathcal$\{$R$\}\backslash )$ be the region bounded by the curves $\backslash ($ x$=$y$^\{2\}\backslash )$ and $\backslash ($ y$=$x$-2\backslash ).$

Set up an integral to compute the volume of the solid generated by rotating $\backslash (\backslash$mathcal$\{$R$\}\backslash )$ about the $\backslash ($ y $\backslash )-$axis. Do not integrate.