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Math Help - tough integral

  1. #1
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    tough integral

    integrate ((10e^(-5000t))*(50(1-e^(-5000t)))) dt from 0 to 1

    I got as far as :

    ((-1/5000)*500e^(-5000t))-500*integral((-1/e^(5000t))^2 dt

    But I cant figure out the integral of (-1/e^-5000t)^2. Please, Can anyone show me how to do this ?
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  2. #2
    Grand Panjandrum
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    Re: tough integral

    Quote Originally Posted by frankinaround View Post
    integrate ((10e^(-5000t))*(50(1-e^(-5000t)))) dt from 0 to 1

    I got as far as :

    ((-1/5000)*500e^(-5000t))-500*integral((-1/e^(5000t))^2 dt

    But I cant figure out the integral of (-1/e^-5000t)^2. Please, Can anyone show me how to do this ?
    \left(-\frac{1}{e^{5000t}}\right)^2=e^{-10000t}

    CB
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  3. #3
    Grand Panjandrum
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    Re: tough integral

    Quote Originally Posted by frankinaround View Post
    integrate ((10e^(-5000t))*(50(1-e^(-5000t)))) dt from 0 to 1

    I got as far as :

    ((-1/5000)*500e^(-5000t))-500*integral((-1/e^(5000t))^2 dt

    But I cant figure out the integral of (-1/e^-5000t)^2. Please, Can anyone show me how to do this ?
    You are making things difficult for yourself by not simplifying this integral as much as possible before trying to evaluate it.

    \int_0^1 (10e^{-5000t})(50(1-e^{-5000t})dt=500\int_0^1e^{-5000t}(1-e^{-5000t})\;dt

    Now you may notice that the integrand is a multiple of the derivative of 1-e^{-5000t}, and so can be integrated immediately. Or you could make the substitution u=5000t first, then make the observation...

    CB
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