IMathAS-libretexts

A solid is constructed between the lines

\displaystyle {x}={a}

\displaystyle {x}={b}

, the graph of

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

and the x-axis so that the cross-sections of the solid are circles perpendicular to the x-axis, as shown in the figure.

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

$\displaystyle {\int_{{a}}^{{b}}}\pi{\left({f{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}\frac{\pi}{{2}}{\left({f{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}\frac{\pi}{{4}}{\left({f{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}{4}\pi{\left({f{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$

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