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Math Help - integrate

  1. #1
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    integrate

    if f is continuous and integrating from 0 to 4 f(x)dx =10 find what integrating from 0 to 2 f(2x)dx is
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  2. #2
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    Re: integrate

    Quote Originally Posted by pnfuller View Post
    if f is continuous and integrating from 0 to 4 f(x)dx =10 find what integrating from 0 to 2 f(2x)dx is

    Let u=2x~\&~du=2dx so \begin{array}{*{20}c}   x &\vline &  0 &\vline &  2  \\\hline   u &\vline &  0 &\vline &  4  \\ \end{array} .

    So \int_0^2 {2f(2x)dx}  = \int_0^4 {f(u)du}
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  3. #3
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    Re: integrate

    wouldn't it be 1/2f(2x) and do you have to do anything else to solve for what it equals like f(x)=10 in the first part, how do you find what f(2x) equals?
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  4. #4
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    Re: integrate

    Quote Originally Posted by pnfuller View Post
    wouldn't it be 1/2f(2x) and do you have to do anything else to solve for what it equals like f(x)=10 in the first part, how do you find what f(2x) equals?

    Why don't you try this for yourself?

    The is simple algebra, \int_0^2 {2f(2x)dx}  = \int_0^2 {f(2x)\left( {2dx} \right)} .

    If \int_a^b {f(t)dt}  = C THEN \int_{u(a)}^{u(b)} {f(u)du}  = C
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