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    Calculating the length of a curve.

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    Find the length of the curve y=e^-x, 0<_x<_1

    © BrainMass Inc. brainmass.com February 24, 2021, 2:12 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/calculating-the-length-of-a-curve-7263

    Solution Preview

    By definition length of curve:

    l = integration(0,1) [sqrt{ 1 + (dy/dx)^2}] dx
    here dy/dx = - e^(-x)
    => l= integ(0,1)[ sqrt{1 + {-e^(-x)}^2}] dx
    => l = int(0,1) [sqrt{1 + e^(-2x)}] ...

    Solution Summary

    The length of a curve is calculated.

    $2.19

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