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Math Help - U-sub definite integral

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    U-sub definite integral

    The integral on 0 to 8 of g(u)du = 15

    What is the integral on 0 to 64 of g(t/8)?

    What is the integral on 0 to 8 of g(8-t)?
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    Quote Originally Posted by AngloSaxonProtestant View Post
    The integral on 0 to 8 of g(u)du = 15

    What is the integral on 0 to 64 of g(t/8)?

    What is the integral on 0 to 8 of g(8-t)?
    \int_{0}^{64}g\left(\frac{t}{8} \right)dt

    let u=\frac{t}{8} \implies du=\frac{1}{8}dt \iff 8du=dt

    Now we need to change the limits of integration  u =\frac{t}{8}

    When t=0 we get  u =\frac{0}{8}=0

    When t=64 we get  u =\frac{64}{8}=8

    Now we sub in to get

    \int_{0}^{64}g\left(\frac{t}{8} \right)dt=\int_{0}^{8}g(u)(8du)=8\int_{0}^{8}g(u)d  u=8\cdot 15=120

    Try the same thing on the next one.

    Good luck
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