IMathAS-libretexts

A solid is contructed so that one side is the region between the lines

\displaystyle {x}={a}

\displaystyle {x}={b}

, the graph of

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

and the x-axis, and the cross-sections of the solid perpendicular to the x-axis are rectangles with base 8 (as shown in the figure).

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

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

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