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Math Help - Integral Problems.

  1. #1
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    Integral Problems.

    Hey everybody,

    This is my first post here on mathhelpforum, anyways.

    I was gone 2 days from class, and we started doing integrals with trig substitutions. I CANNOT for the life of me get one of these right. To be honest, I'm getting extremely frustrated.

    Here is a picture of one of the problems. (I don't know how to use the math software.)

    Integral Problems.-2012-03-15_19-46-20_115-1.jpg

    Here's what I'm trying.

    I'm using the trig property (1 + tan^2 = sec^2)

    I then did

    x = 3tan(x)
    so dx = 3sec^2(x)

    And from there, after substiting x and replacing dx with 3sec^2(x), I simplified it to the integral of sec of x, which I thought was sec(x)tan(x), however, that's not even close to the answer in the back.

    I really need help on this,

    Thanks guys.
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  2. #2
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    Re: Integral Problems.

    The derivative of sec(x) is sec(x)tan(x), but I believe the integral is $\ln{\vert sec(x)+tan(x)\vert}$
    Last edited by browni3141; March 15th 2012 at 05:15 PM. Reason: added abs
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  3. #3
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    Re: Integral Problems.

    Quote Originally Posted by browni3141 View Post
    The derivative of sec(x) is sec(x)tan(x), but I believe the integral is $\ln{\vert sec(x)+tan(x)\vert}$
    Well that explains that part, but I'm still getting the wrong answer. I'm getting ln ( sqr(x^2+9)/3 + x/3) + C, when the answer is ln(sqr(2) + 1).

    Thanks again.
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  4. #4
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    Re: Integral Problems.

    Quote Originally Posted by CalcAustin View Post
    Well that explains that part, but I'm still getting the wrong answer. I'm getting ln ( sqr(x^2+9)/3 + x/3) + C, when the answer is ln(sqr(2) + 1).

    Thanks again.
    You took the indefinite integral, where the problem is asking for a definite integral from 0 to 3.
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