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Math Help - Convergence of an improper integral

  1. #1
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    Convergence of an improper integral

    I cant figure out how to answer this calculus problem. I'm having trouble actually calculating the integral.

    a) (integral from 0 to 1) sin(x+1/x)dx

    I haven't been able to answer that, theres a part b that I havent tried yet since the first one has been giving me problems.

    b) (integral from 0 to 1) sin^2(x+1/x)
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    Quote Originally Posted by blorpinbloo View Post
    I cant figure out how to answer this calculus problem. I'm having trouble actually calculating the integral.

    a) (integral from 0 to 1) sin(x+1/x)dx

    I haven't been able to answer that, theres a part b that I havent tried yet since the first one has been giving me problems.

    b) (integral from 0 to 1) sin^2(x+1/x)
    Try the sine of a sum formula.
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  3. #3
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    Quote Originally Posted by blorpinbloo View Post
    I cant figure out how to answer this calculus problem. I'm having trouble actually calculating the integral.

    a) (integral from 0 to 1) sin(x+1/x)dx

    I haven't been able to answer that, theres a part b that I havent tried yet since the first one has been giving me problems.

    b) (integral from 0 to 1) sin^2(x+1/x)
    Specify it:
    x+\frac{1}{x} or \frac{x+1}{x} ?!
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  4. #4
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    My bad, its x+(1/x)
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    Quote Originally Posted by blorpinbloo View Post
    My bad, its x+(1/x)
    It can not be expressed in terms of elementary functions.
    http://www.wolframalpha.com/input/?i...%281%2Fx%29%5D
    Did you post all informations ?
    Last edited by General; January 14th 2010 at 01:22 PM.
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    Quote Originally Posted by General View Post
    It can not be expressed in terms of elementary functions.
    Integrate sin[x+(1/x)] - Wolfram|Alpha
    Did you post all informations ?
    Could this be integrated?

    sin\left(x+\frac{1}{x}\right)=sin(x)cos\left(\frac  {1}{x}\right)+sin\left(\frac{1}{x}\right)cos(x)

    I'm not very good at integration, so I can't always tell right away. I would have to work through it.
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  7. #7
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    Nevermind that, I didn't notice your wolfram link.
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  8. #8
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    Quote Originally Posted by adkinsjr View Post
    Could this be integrated?

    sin\left(x+\frac{1}{x}\right)=sin(x)cos\left(\frac  {1}{x}\right)+sin\left(\frac{1}{x}\right)cos(x)

    I'm not very good at integration, so I can't always tell right away. I would have to work through it.
    No.
    Wolfaram\alpha integrator considers all cases.
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  9. #9
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    The question was "Show that the following improper integrals both converge." I assumed you had to calculate the integral because that's what the section was about, but I suppose there may be another way to solve it without calculating it.
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