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Math Help - Integral Type Problem

  1. #1
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    Question Integral Type Problem

    Find the value of k to the nearest integer such that the line x=k divides the area under f(x)=(x^3)/36 - x + 15 on [0,20] into two equal areas.

    I set up an integral with the integrand being the f(x) from 0 to 20 and I got 1,211.11 then I divided by two which is 605.556. I am not quite sure what to do from here. Can someone shed some light on this problem? Thanks!
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  2. #2
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    \int_0^k f(x) \, dx = \frac{1}{2} \int_0^{20} f(x) \, dx

    \frac{k^4}{144} - \frac{k^2}{2} + 15k = \frac{1}{2} \int_0^{20} f(x) \, dx

    solve for k
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