1. Using washers, the volume is given by the integral
We're using washers whose centers depend on the value of , hence we integrate with respect to
2. The area of the given region is given by the integral
To compute the integral, first consider the substitution , or so that . Then and , so the integral is equivalently
Integrate by parts, taking
so that
and , so the area is
For the remaining integral, substitute , so that . Then and :
(notice that the integral is improper)