IMathAS-libretexts

A solid is constructed between the graphs of

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

and

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

and the lines

\displaystyle {x}={a}

and

\displaystyle {x}={b}

so that the cross-sections perpendicular to the x-axis are squares, as shown in the figure.

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

$\displaystyle {\int_{{a}}^{{b}}}{\left({f{{\left({x}\right)}}}-{g{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}\frac{{1}}{{4}}{\left({f{{\left({x}\right)}}}-{g{{\left({x}\right)}}}\right)}^{{2}}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}\frac{{1}}{{4}}{\left[{\left({f{{\left({x}\right)}}}\right)}^{{2}}-{\left({g{{\left({x}\right)}}}\right)}^{{2}}\right]}\ {\left.{d}{x}\right.}$
$\displaystyle {\int_{{a}}^{{b}}}{\left[{\left({f{{\left({x}\right)}}}\right)}^{{2}}-{\left({g{{\left({x}\right)}}}\right)}^{{2}}\right]}\ {\left.{d}{x}\right.}$

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