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Math Help - [SOLVED] derivative of integral

  1. #1
    Bop
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    [SOLVED] derivative of integral

    Hello, I want to calculate the derivative of f(x), where:

    f(x)=\int^x_{sin{x}} e^{t^2}dt

    I don't have many ideas how to start with this, I had thought maybe transforming it into a taylor series and then evaluate and calculate its derivative, what do you think?


    Thank you.
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  2. #2
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    Quote Originally Posted by Bop View Post
    Hello, I want to calculate the derivative of f(x), where:

    f(x)=\int^x_{sin{x}} e^{t^2}dt

    I don't have many ideas how to start with this, I had thought maybe transforming it into a taylor series and then evaluate and calculate its derivative, what do you think?


    Thank you.

    Let F(x) be any primitive function of e^{t^2} (why does it exist?) , then f(x)=\int\limits^x_{sin{x}} e^{t^2}dt=F(x)-F(\sin x)\Longrightarrow f'(x)=F'(x)-\cos xF'(\sin x)= ...

    The above is just a simple particular case of the Leibnitz (differentiation under the sign of) integral rule.

    Tonio
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  3. #3
    Bop
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    Ok, thank you very much.
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