IMathAS-libretexts

The graph of

\displaystyle {y}={f{{\left({x}\right)}}}

between the lines

\displaystyle {x}={a}

and

\displaystyle {x}={b}

is rotated around the line

\displaystyle {y}={8}

to form a solid, as shown in the figure (where

\displaystyle {K}={8}

).

Which of the following integrals represents the volume of this solid?

$\displaystyle {\int_{{a}}^{{b}}}\pi{\left({f{{\left({x}\right)}}}-{8}\right)}^{{2}}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}\pi{\left[{\left({f{{\left({x}\right)}}}\right)}^{{2}}-{64}\right]}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}{2}\pi{x}{\left[{f{{\left({x}\right)}}}-{8}\right]}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}\pi{\left({f{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$