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Math Help - Fundamental Theorum of Integral

  1. #1
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    Fundamental Theorum of Integral

    Find f and a that
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  2. #2
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    Quote Originally Posted by camherokid View Post
    Find f and a that
    6 + integal_{t=a to x} f(t)/t^2 dt = 2 sqrt(x)

    1. When x=a the integral is zero, so:

    6 = 2 sqrt(a),

    or a = 9.

    2. Differentiate (by the FTC d/dx[integal_{t=a to x} f(t)/t^2 dt] = f(x)/x^2)

    f(x)/x^2 = 1/sqrt(x)

    so: f(x) = x^{3/2}.

    RonL
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