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Math Help - Integration Question as Part of a Differential Equation

  1. #1
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    Integration Question as Part of a Differential Equation

    I am posting this here because I don't need help on the whole DE just on this integral..

    Here it is:





    Please explain.. I can't come up with pi in the denominator..
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  2. #2
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    Quote Originally Posted by eingeist View Post
    I am posting this here because I don't need help on the whole DE just on this integral..

    Here it is:


    Please explain.. I can't come up with pi in the denominator..
    Excause me, Did you try the substitution u=\frac{-\pi}{x} ?
    Its helpful, Trust me .
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  3. #3
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    I see... Would I pull 1/pi out in front of the integral? Or would I simply pull pi out since du = pi/x^2...

    Seems like it would have to be 1/pi to get that pi in the denominator.
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  4. #4
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    Quote Originally Posted by eingeist View Post
    I see... Would I pull 1/pi out in front of the integral? Or would I simply pull pi out since du = pi/x^2...

    Seems like it would have to be 1/pi to get that pi in the denominator.
    put \pi inside the integral, and \frac{1}{\pi} outside the integral.

    Because they will cancel each other.
    i.e. you just multiplied by 1.
    See this:
    \int f(x) dx=\int (1) f(x) dx=\int \frac{\pi}{\pi} f(x) dx
    =\int (\pi) (\frac{1}{\pi}) f(x) dx = \frac{1}{\pi} \int (\pi) f(x) dx.

    By the way, du=\frac{\pi}{x^2} \;\ {\color{red} dx}
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