Mathematics

Mathematics

Problem

The region bounded by y=2x−x2y=2x-x^{2} and the xx-axis for 0≤x≤20\le x\le2 is revolved about the line y=−2y=-2. Which of the following integrals correctly represents the volume of the solid? a) V=π∫02[(2x−x2)2−22] dxV=\pi\displaystyle\int_{0}^{2}\Big[(2x - x^{2})^{2}-2^{2}\Big]\,dx b) V=π∫02[(2x−x2+2)2] dxV=\pi\displaystyle\int_{0}^{2}\Big[(2x - x^{2}+2)^{2}\Big]\,dx c) V=π∫02[(2x−x2+2)2−22] dxV=\pi\displaystyle\int_{0}^{2}\Big[(2x - x^{2}+2)^{2}-2^{2}\Big]\,dx d) V=π∫02[(2x−x2+2)2−(2x−x2)2] dxV=\pi\displaystyle\int_{0}^{2}\Big[(2x - x^{2}+2)^{2}-(2x - x^{2})^{2}\Big]\,dx

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