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Question Number 99278 by Rio Michael last updated on 19/Jun/20

$$x0246810$$$$f\left(x\right)2.43.64.96.98.011.9$$$$\mathrm{Given}\mathrm{the}\mathrm{curve}y=f\left(x\right),\mathrm{with}\mathrm{corresponding}\mathrm{values}\mathrm{of}$$$$f\left(x\right)\mathrm{at}\mathrm{certain}x\mathrm{values}.\mathrm{The}\mathrm{curve}y=f\left(x\right)\mathrm{is}\mathrm{rotated}$$$$\mathrm{at}\mathrm{an}\mathrm{angle}\mathrm{of}2\pi \mathrm{about}\mathrm{the}\mathrm{x}-\mathrm{axis}.\mathrm{Find}$$$$\left(1\right)\mathrm{The}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{surface}\mathrm{generated}\mathrm{using}{\mathrm{simpson}}^{\prime }\mathrm{s}\mathrm{rule}.$$$$\left(2\right)\mathrm{The}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{surface}\mathrm{generated}\mathrm{using}{\mathrm{simpson}}^{\prime }\mathrm{s}\mathrm{rule}.$$

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