March 28, 2017

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Find the volume of the solid generated by revolving the triangular region with vertices (1,1), (b,1), and (1,h) about:
a) the x-axis
b) the y-axis

  • Calculus II - ,

    If a<1 and b<1 we get
    Using discs:
    pi*Int(R^2 - r^2) dx [b,1]
    R = 1
    r = y = (a-1)(x-b)/(1-b) + 1

    = pi/3 (a-1)(a+2)(b-1)

    Using shells:
    2pi*Int(rh)dy [a,1]
    r = y
    h = 1-x = 1 - [(1-b)(y-1)/(a-1) + b]

    = pi/3 (a-1)(a+2)(b-1)

    If a or b > 1, then change integration limits and (1-a) -> (a-1), but the answer is the same

    Thank you, Wolframalpha!

  • Calculus II - PS - ,

    oh - that's just around the x-axis. Good luck on the y-axis. By symmetry, the results should look quite similar.

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