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Math Help - centroid

  1. #1
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    centroid

    Find the centroid of the region bounded by y = lnx, y = 0, 1 >= x >= e

    What I did was found the area by taking the integral of lnx and evaluating it @ 1 and e.
    Then I put it in the formula to find x bar and y bar.
    I got an undefined numbers for x and -1/3 for y.

    Does anyone know how to correctly solve this problem?
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  2. #2
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    Quote Originally Posted by sleepiiee View Post
    Find the centroid of the region bounded by y = lnx, y = 0, 1 >= x >= e

    What I did was found the area by taking the integral of lnx and evaluating it @ 1 and e.
    Then I put it in the formula to find x bar and y bar.
    I got an undefined numbers for x and -1/3 for y.

    Does anyone know how to correctly solve this problem?
    \bar x =\frac{\int_{1}^{e}x\ln(x)dx}{\int_{1}^{e}\ln(x)dx  }

    Both of the above are integrated by parts to give

    \bar x =\frac{\frac{1}{4}+\frac{1}{4}e^{2}}{1}

    \bar y =\frac{\int_{1}^{e}[\ln(x)]^2dx}{\int_{1}^{e}\ln(x)dx}

    The top in integration by parts twice and the bottom is 1 from above to give

    \bar y =\frac{e-2}{1}=e-2
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