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Math Help - integrable problem

  1. #1
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    integrable problem

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  2. #2
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    Let me show you something similar. Perhaps apply it to yours.

    Let's show that \frac{d}{dx}\int_{a}^{g(x)}f(t)dt=f(g(x))g'(x)

    Let u=g(x), then

    \frac{d}{dx}\int_{a}^{g(x)}f(t)dt

    =\frac{d}{dx}\int_{a}^{u}f(t)dt

    =\frac{d}{du}\left[\int_{a}^{u}f(t)dt\right]\frac{du}{dx}

    =f(u)g'(x)=f(g(x))g'(x)
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  3. #3
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    property

    i know this property.

    so we can directly deduce the conclusion from this property,right ????
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  4. #4
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    I believe so. Give it a whirl.
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  5. #5
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    cant doo

    still can get that result...

    can u show it explicitly?
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  6. #6
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    how

    here, i got g(x)= x, a= 0,


    <br />

    " alt="=\frac{d}{dx}\int_{0}^{x}f(t)dt
    " />

    =f(x)*g'(x)=f(x)

    cant continue...or i did

    =f(g(x)) * 1

    integrate both sides , that integral= f(g(x)) * x, but how can u ignore g(x)=x?
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