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Math Help - analysis help

  1. #1
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    analysis help

    Suppose that f is a continuous function on R and define a function F on [0, infinity) by f(x)= the integral of f from x to -x. Find a simple expression for F'(x).
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  2. #2
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    Quote Originally Posted by friday616 View Post
    Suppose that f is a continuous function on R and define a function F on [0, infinity) by f(x)= the integral of f from x to -x. Find a simple expression for F'(x).

    So F(x):=\int\limits_{-x}^xf(t)\,dt

    Let us take a primitive of f: G'(t)=f(t)\,\,\forall,t. By the Fundamental theorem of Integral Calculus we get that \int\limits_a^bf(t)\,dt=G(b)-G(a)\,,\,\,\forall\,a\,,\,b, so:

    F(x)=G(x)-G(-x)\Longrightarrow \,F'(x)=G'(x)+G'(-x)=...

    Tonio
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