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9 February, 13:36

If the infinite curve y = e-9x, x ≥ 0, is rotated about the x-axis, find the area of the resulting surface.

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  1. 9 February, 14:06
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    We are given with the equation

    y = e^-9x with the restriction of x ≥ 0

    If rotated about the x-axis the area of the resulting surface is

    A = π ∫ y² dx

    Substituing

    A = π ∫ (e^-9x) ² dx

    A = π ∫ e^-18x dx

    The limits are from 0 to positive infinity.
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