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Math Help - Finding Arc Length of a Function

  1. #1
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    Question Finding Arc Length of a Function

    I'm having some trouble with these:

    1. Find the arc length of the function: y^2 = 4(x+4)^3 from 0 to 2

    2. Find the arc length of the function: y = e^x from 0 to 1

    Thank you very much for any assistance
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  2. #2
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    Lexington, MA (USA)
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    Hello, coolio!

    The first one is straight-forward.
    Exactly where is your difficulty?


    1. Find the arc length of the function: y^2 \:= \:4(x+4)^3 from 0 to 2
    Formula: . L \;=\;\int^b_a\sqrt{1 + \left(\frac{dy}{dx}\right)^2}\,dx


    We have: . y \;=\;2(x+4)^{\frac{3}{2}}

    . .Then: . \frac{dy}{dx} \:=\:3(x+4)^{\frac{1}{2}}

    . .And: . 1 +\left(\frac{dy}{dx}\right)^2 \;=\;1 + 9(x+4) \;=\;9x+37

    . . Hence: . \sqrt{1+ \left(\frac{dy}{dx}\right)^2} \;=\;\sqrt{9x+37}


    Then we have: . L \;=\;\int^2_0(9x+37)^{\frac{1}{2}}\,dx

    Can you finish it?

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  3. #3
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    Thanks soroban, I tried multiplying out the polynomial and it just turned into a huge mess. I understand now
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