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Math Help - Very simple question on "definite integrals"

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    Very simple question on "definite integrals"

    Very simple question on "definite integrals"-2011-08-17-5.38.28-pm.png
    At this stage, can I simple plug in 1 and 0 into the exponential to get the answer?
    By doing so, I would get 4/3. But the model answer is 4/[3xln(5)].
    Thanks!
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  2. #2
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    Re: Very simple question on "definite integrals"

    No, you need to perform the integration first.
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    Re: Very simple question on "definite integrals"

    How to integrate that exponential function? I thought it remains the same after integration
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    MHF Contributor Siron's Avatar
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    Re: Very simple question on "definite integrals"

    You can use a small substitution if you want, let y\cdot \ln(5)=t \Rightarrow dy=\frac{dt}{\ln(5)} therefore:
    \frac{1}{3\cdot \ln(5)}\int_{0}^{1} e^{t}dt= ...
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    Re: Very simple question on "definite integrals"

    Quote Originally Posted by Siron View Post
    You can use a small substitution if you want, let y\cdot \ln(5)=t \Rightarrow dy=\frac{dt}{\ln(5)} therefore:
    \frac{1}{3\cdot \ln(5)}\int_{0}^{1} e^{t}dt= ...
    This agrees with the result that you would get by first rewriting the integrand as e^{\ln(5^y)} = 5^y, then integrating. Of course, the "rule" for integrating a^x for a > 0 comes from writing it in base e!
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