Exam 7: Extension E: Differential Equations

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Find the area of the surface obtained by rotating the circle Find the area of the surface obtained by rotating the circle   about the line  about the line Find the area of the surface obtained by rotating the circle   about the line

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E

Find the area of the surface obtained by revolving the graph of y = Find the area of the surface obtained by revolving the graph of y =   on [0,1] about the x-axis. on [0,1] about the x-axis.

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4 π\pi

Find the area of the surface obtained by rotating the curve about the Find the area of the surface obtained by rotating the curve about the   -axis.   -axis. Find the area of the surface obtained by rotating the curve about the   -axis.

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Find the area of the surface obtained by rotating the curve about the y-axis. Find the area of the surface obtained by rotating the curve about the y-axis.

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Find the area of the surface obtained by rotating the curve about the x-axis. Find the area of the surface obtained by rotating the curve about the x-axis.

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Find the area of the surface obtained by revolving the given curve about the y-axis. x = Find the area of the surface obtained by revolving the given curve about the y-axis. x =   on [0,2] on [0,2]

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Set up,but do not evaluate,an integral for the area of the surface obtained by rotating the curve about the given axis. Set up,but do not evaluate,an integral for the area of the surface obtained by rotating the curve about the given axis.   y-axis y-axis

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