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Math Help - Graphing Integrals by hand

  1. #1
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    Graphing Integrals by hand

    Hi, I was wondering how to sketch the graph of an integral. The function is:

    f(x)=integral(lower limit 1 upper limit x) 2t/t^3+1

    I was thinking that I could take the anti-derivative, but would that become the derivative f'(x) by FTC. Thanks for any help guys!
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  2. #2
    Senior Member vincisonfire's Avatar
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    In general you have \int_{a}^{x} f(t)dt = F(x)-F(a) by the fundamental theorem of calculus. This is a function which you can graph.
    Now you must use the partial fraction theorem to get that  \frac{2t}{t^3+1} = -\frac{2}{3(t+1)}+\frac{2t+2}{3(t^2-t+1)}
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