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Math Help - integration question

  1. #1
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    integration question

    right now i'm stuck on this integration problem. it's integrating (1/theta^2)cos(1/theta). any suggestions??
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  2. #2
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    Hello, needhelp101!

    \int \frac{\cos\left(\frac{1}{\theta}\right)}{\theta^2}  \,d\theta

    We have: . \int \cos\left(\theta^{-1}\right)\,\left(\theta^{-2}d\theta\right)

    Let u \:=\:\theta^{-1} \quad\Rightarrow\quad du \:=\:-\theta^{-2}d\theta \quad\Rightarrow\quad \theta^{-2}d\theta \:=\:-du

    Substitute: . \int \cos u\,(-du) \;=\;-\!\!\int\cos u\,du

    Got it?

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  3. #3
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    yup. i got it now. thanks for the help. i really appreciate it.
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  4. #4
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    Quote Originally Posted by needhelp101 View Post
    right now i'm stuck on this integration problem. it's integrating (1/theta^2)cos(1/theta). any suggestions??
    \int\theta^{-2}\cos{\theta^{-1}}d\theta

    Substitution:

    u=\theta^{-1}

    -du=\theta^{-2}d\theta

    \int\theta^{-2}\cos{\theta^{-1}}d\theta=-\int\cos{u}\;du

    =-\sin{u}

    =-\sin{\theta^{-1}}

    Check the solution by taking the derivative:

    -\frac{d}{d\theta}\sin{\theta^{-1}}=\theta^{-2}\cos{\theta^{-1}}

    Looks good!
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