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Arc Length and Surface Area worksheets

Set up x- and y-direction arc length and surface-area integrals with friendly exact evaluation cases.

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Set up x- and y-direction arc length and surface-area integrals with friendly exact evaluation cases.

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Choose the correct differential and nonnegative radius for geometric integral applications.

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Math SheetNameScoreTeacherDateArc Length and Surface AreaWrite the correct x- or y-direction integral. Evaluate only the selected friendly exact families; otherwise the exact setup is the final answer.1.The quarter circle y=sqrt(196-x^2), 0<=x<=14, is revolved about the x-axis. Set up the surface-area integral.2.For y=2/3(x+1)^(3/2), 0<=x<=5, find the exact arc length.State assumptions, domains, units, and approximation methods.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateArc Length and Surface AreaWrite the correct x- or y-direction integral. Evaluate only the selected friendly exact families; otherwise the exact setup is the final answer.3.For x=2/3(y+1)^(3/2), 0<=y<=9, set up the arc-length integral.4.The quarter circle x=sqrt(196-y^2), 0<=y<=14, is revolved about the y-axis. Find the exact surface area.State assumptions, domains, units, and approximation methods.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateArc Length and Surface AreaWrite the correct x- or y-direction integral. Evaluate only the selected friendly exact families; otherwise the exact setup is the final answer.5.The quarter circle y=sqrt(36-x^2), 0<=x<=6, is revolved about the x-axis. Set up the surface-area integral.6.For x=2/3(y+1)^(3/2), 0<=y<=9, find the exact arc length.State assumptions, domains, units, and approximation methods.math-sheet.comPage 3 of 3

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