Let be a constant

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

Problem

Let d>3d>3 be a constant. Region SS is bounded by y=3y=3, y=xy=x, and x=0x=0. When SS is revolved about the horizontal line y=dy=d, the volume is V(d)V(d). Which of the following gives V(d)V(d)? (a) V(d)=π∫03((d−x)−(d−3)) dx\displaystyle V(d)=\pi\int_{0}^{3}\bigl((d-x)-(d-3)\bigr)\,dx (b) V(d)=π∫03((d−x)2−(d−3)2) dx\displaystyle V(d)=\pi\int_{0}^{3}\bigl((d-x)^{2}-(d-3)^{2}\bigr)\,dx (c) V(d)=π∫03((d−3)2−(d−x)2) dx\displaystyle V(d)=\pi\int_{0}^{3}\bigl((d-3)^{2}-(d-x)^{2}\bigr)\,dx (d) V(d)=2π∫03x (3−x) dx\displaystyle V(d)=2\pi\int_{0}^{3}x\,(3-x)\,dx

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