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Integral Calculus

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Find the area of the surface generated by revolving the given curve about the y-axis.

8xy^2=2y^6+1 , 1<=y<=2.

thank you so much.. :)

  • Integral Calculus -

    You need x as a function of y to do the integration.

    In this case, x(y) = 1/(8y^2) + (y^4)/4

    To get the surface area, evaluate:

    Integral of 2 pi x(y) dy
    (y = 1 to 2)

    The indefinite integral is
    2 pi [-1/(24y^3) + y^5/20]
    = pi[(y^5)/10 - 1/(24y^3)]
    Evaluate it at y=2 and y=1, and take the difference. Check my math.

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