Math

The region enclosed by the curve y = ex, 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.
How do you do this?

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  1. assume you mean y = e^x
    at x = 0, y = e^0 = 1
    at x = 1, y = e^1 = e = 2.718

    area of circle at x = pi e^2x
    so I want integral from x = 0 to x = 1 of
    pi e^2x dx
    well to make it easy let z = 2x
    then dx = dz/2
    so
    if x = 0, z = 0
    if x = 1, z = 2
    so I want the integral from z = 0 to z = 2 of
    (1/2) e^z dz
    = (1/2) e^z at z = 2 - at z = 0
    =(1/2)(e^2 -1)

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  2. (pi/2)(e^2-1)

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