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March 30, 2017

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The region enclosed by the curve y =e^x, the x-axis, and the lines x=0 and x=1 is revolved about the x-axis. Find the volume of the resulting solid formed.

  • Solids of Revolution - ,

    just use discs:

    v = integral(pi*r^2)dx from x=0 to 1
    where r = y = e^x
    v = pi*Integral(e^2x dx) [0,1]
    = pi(1/2 e^2x) [0,1]
    = pi(e^2/2 - 1/2)
    = pi/2 (e^2 - 1)

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