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Math Help - Finding a local Max of an Integral with Variable Limits

  1. #1
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    Finding a local Max of an Integral with Variable Limits

    Given:

    \int_0^x \frac{ t^2 - 4 }{ 1+\cos^2(t)} dt

    at what value of x does the local maximum of f(x) occur?

    I tried this, but it isn't correct.

    (x^2-4)/(1+cos^2(x))

    Do I not just plug in the variable at the top for t and subtract the same function replacing t with 0? What am I missing?
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  2. #2
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    Quote Originally Posted by derekjonathon View Post
    Given:

    \int_0^x \frac{ t^2 - 4 }{ 1+\cos^2(t)} dt

    at what value of x does the local maximum of f(x) occur?

    I tried this, but it isn't correct.

    (x^2-4)/(1+cos^2(x))

    Do I not just plug in the variable at the top for t and subtract the same function replacing t with 0? What am I missing?
    F(x) = \int_0^x \frac{ t^2 - 4 }{ 1+\cos^2(t)} \, dt \Rightarrow \frac{dF}{dx} = \frac{ x^2 - 4 }{ 1+\cos^2(x)}. Now solve \frac{dF}{dx} = 0 etc.
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