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Math Help - Integration

  1. #1
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    Integration

    (\int f(x), x, 0, 9) = 4 then (\int f(3x), x, 0 ,3) =

    Equals 4/3 but how do you do it using antidifferentiation and not by showing examples?
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  2. #2
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    let

    u=\frac{x}{3} \implies du=\frac{dx}{3}

    and don't forget the variable of integration is a dummy variable.

    try to sub this into the first integral.
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  3. #3
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    so does that mean that 1/3 applies to the first integral. And also the integral is 0, 9 on the first integral and 0,3 on the second..... how does that work out?




    Quote Originally Posted by TheEmptySet View Post
    let

    u=\frac{x}{3} \implies du=\frac{dx}{3}

    and don't forget the variable of integration is a dummy variable.

    try to sub this into the first integral.
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  4. #4
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    and bring the 3 out from the 3x?
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  5. #5
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    You are given that \int_0^9 f(x)dx= 4 which, since we can always change a dummy variable, is the same as \int_0^9 f(u)du= 4. To integrate \int_0^3 f(3x)dx, let u= 3x so x= u/3 as TheEmptySet suggested. Then dx= (1/3)du. When x= 0, u= 0. When x= 3, u= 9. The integral becomes
    \int_0^9 f(u)((1/3)du)= \frac{1}{3}\int_0^9 f(u)du
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