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**CaptainBlack** The volume of revolution can be envisaged as approximatly composed of disks of radius $\displaystyle \sqrt{x}$ and thickness $\displaystyle \delta x$ , and hence volume of each disk is $\displaystyle \pi |x| \delta x$. Then the volume of the solid of revolution is approximatly the sum of the volumes of the disks comprising the solid, or in the limit the integral:

$\displaystyle V=\int_2^7 \pi |x|\ dx$

and as $\displaystyle x$ is positive over the range of integration we can drop the $\displaystyle |.|$ to get:

$\displaystyle V=\int_2^7 \pi x\ dx$

CB