Which integral expression represents the volume V of a solid obtained by revolving…

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Which integral expression represents the volume V of a solid obtained by revolving the region between the curves x = R(y) and x = r(y), where R(y) ≥ r(y) ≥ 0 for a ≤ y ≤ b, about the y-axis? (a) V=π∫ab[R(y)]2 dy\displaystyle V = \pi\int_{a}^{b}[R(y)]^{2}\,dy (b) V=π∫ab(R(y)−r(y))2 dy\displaystyle V = \pi\int_{a}^{b}\bigl(R(y)-r(y)\bigr)^{2}\,dy (c) V=π∫ab( [R(y)]2−[r(y)]2 ) dy\displaystyle V = \pi\int_{a}^{b}\left(\,[R(y)]^{2}-[r(y)]^{2}\,\right)\,dy (d) V=π∫ab([R(y)]2+[r(y)]2) dy\displaystyle V = \pi\int_{a}^{b}\left([R(y)]^{2}+[r(y)]^{2}\right)\,dy

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