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

    So $\displaystyle \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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    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, $\displaystyle \int_0^2 {2f(2x)dx} = \int_0^2 {f(2x)\left( {2dx} \right)} $.

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