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Math Help - Intergral help

  1. #1
    Junior Member
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    Question Intergral help

    Over what open interval does the formula F(x)=[int (from 1 to x) dt/t]

    represent an antiderivative of f(x)=1/x? and find a point where the graph of F crosses the x-axis.

    I don't even how to start calculating this problem.

    Thank you
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by noppawit View Post
    Over what open interval does the formula F(x)=[int (from 1 to x) dt/t]

    represent an antiderivative of f(x)=1/x? and find a point where the graph of F crosses the x-axis.

    I don't even how to start calculating this problem.

    Thank you
    hmm, since you are already in the integrals, you should already know the function for which you differentiate it gives \frac{1}{x}.

    let F(x) = \ln x. Then F'(x) = \frac{1}{x}.

    Thus, by FTOC, F(x) = \int_a^x \frac{1}{t} \, dt, where a>0..
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