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Math Help - Calculate the generalized integral

  1. #1
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    Question Calculate the generalized integral

    Calculate the generalized integral

    Calculate the generalized integral-picture-2.png

    Calculate the generalized integral-sugerkuk.jpg


    Am I correct? and then?
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  2. #2
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    Quote Originally Posted by sf1903 View Post
    Calculate the generalized integral

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    Am I correct? and then?

    Sorry to say but you're not even close to correct, and if you wrote the above then I think you need to go back to your general basics on integration:

    \int\frac{x^2-1}{x^4}dx=\int\left(\frac{1}{x^2}-\frac{1}{x^4}\right)dx=-\frac{1}{x}+\frac{1}{3x^3}.

    Now evaluate the above in the integral's limits and make the upper limit tend to \infty ...the answer must be \frac{2}{3}

    Tonio
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  3. #3
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    we can also turn this improper integral into a proper one, so let's put x=\frac1t and the integral becomes \int_{0}^{1}{\left( 1-t^{2} \right)\,dt}=1-\frac{1}{3}=\frac{2}{3}.
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