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    Find the exact length of the curve defined by y=2[(sqrt(x))^(3)]-1=2x^(3/2)-1 from x=0 to x=2. Set up the integral, use the substitution method( reverse chain rule), and express your answer in radical form. (ex sqrt(2), not 2.141).

    © BrainMass Inc. brainmass.com December 24, 2021, 9:54 pm ad1c9bdddf
    https://brainmass.com/math/curves/exact-length-curve-423060

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    Find the exact length of the curve defined by y=2[(sqrt(x))^(3)]-1=2x^(3/2)-1 from x=0 to x=2. Set up the integral, use the substitution method( reverse chain rule), and express your answer in radical form.

    The length of the curve is calculated as:
    So we first find the derivative of the function

    Then the length of the curve from x = 0 to x = 2 is:

    Let . Then,
    Substitute x and dx to the above integral:

    Now substitute x back to indefinite integral in terms of x.

    So the length of the curve from x = 0 to x = 2 is:

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:54 pm ad1c9bdddf>
    https://brainmass.com/math/curves/exact-length-curve-423060

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