IMathAS-libretexts

The region between the lines

\displaystyle {x}={a}

\displaystyle {x}={b}

, the graph of

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

and the x-axis is rotated around the x-axis to form a solid.

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

$\displaystyle {\int_{{a}}^{{b}}}{2}\pi{x}\cdot{f{{\left({x}\right)}}}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}{\left({f{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}\pi{\left({f{{\left({x}\right)}}}\right)}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}\pi{\left({f{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$