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Thread: Definite Integral: int[1,3][(x+1)/(x(x^2+1))]dx (I don't get correct value)

  1. #1

    Definite Integral: int[1,3][(x+1)/(x(x^2+1))]dx (I don't get correct value)

    Ok so I evaluated the indefinite integral and got the right answer but when I plugged in the bounds, I got the wrong answer.



    Calculate the definite integral:

    . . . . .[tex]\displaystyle \int_1^3\, f(x)\, dx\, =\, F(x)\, =\, \int_1^3\, \dfrac{x\, +\, 1}{x\, (x^2\, +\, 1)}\, dx[/tex]



    Computed by Maxima:

    . . .[tex]\displaystyle \int\, f(x)\, dx\, [/tex]

    . . . . . . .[tex]=\, \ln\left(\big|x\big|\right)\, -\, \dfrac{\ln(x^2\, +\, 1)}{2}\, +\, \arctan(x)\, +\, C[/tex]

    . . .[tex]\displaystyle \int_1^3\, f(x)\, dx\, [/tex]

    . . . . . . .[tex]=\, \ln(3)\, -\, \dfrac{\ln(10)}{2}\, +\, \arctan(3)\, +\, \dfrac{2\ln(2)\, -\, \pi}{4}[/tex]

    . . . . . . .[tex]\approx 0.7575409414518656[/tex]




    For the last term I had arctan(1) which is exactly double the last term the int calculator had.

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    Last edited by stapel; 03-03-2018 at 07:48 PM. Reason: Typing out the text in the graphic; creating useful subject line.

  2. #2
    Elite Member stapel's Avatar
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    Quote Originally Posted by Seed5813 View Post
    Ok so I evaluated the indefinite integral and got the right answer but when I plugged in the bounds, I got the wrong answer.



    Calculate the definite integral:

    . . . . .[tex]\displaystyle \int_1^3\, f(x)\, dx\, =\, F(x)\, =\, \int_1^3\, \dfrac{x\, +\, 1}{x\, (x^2\, +\, 1)}\, dx[/tex]



    Computed by Maxima:

    . . .[tex]\displaystyle \int\, f(x)\, dx\, [/tex]

    . . . . . . .[tex]=\, \ln\left(\big|x\big|\right)\, -\, \dfrac{\ln(x^2\, +\, 1)}{2}\, +\, \arctan(x)\, +\, C[/tex]

    . . .[tex]\displaystyle \int_1^3\, f(x)\, dx\, [/tex]

    . . . . . . .[tex]=\, \ln(3)\, -\, \dfrac{\ln(10)}{2}\, +\, \arctan(3)\, +\, \dfrac{2\ln(2)\, -\, \pi}{4}[/tex]

    . . . . . . .[tex]\approx 0.7575409414518656[/tex]




    For the last term I had arctan(1) which is exactly double the last term the int calculator had.
    What did you get when you rearranged your terms to match what the calculator had, and then combined the last two terms into one fraction?

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