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Math Help - Integrtion

  1. #1
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    Integrtion

    Integrate √(5+4x-x^2)

    I dont even know where to begin. Any ideas?
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  2. #2
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    \displaystyle \int \sqrt{5+4x-x^2}dx = \int \sqrt{9-(x-2)^2}dx

    Now use u and trignometric substitution
    Last edited by Educated; October 13th 2010 at 08:50 PM. Reason: Forgot the dx's
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  3. #3
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    Quote Originally Posted by andrewho93 View Post
    Integrate √(5+4x-x^2)

    I dont even know where to begin. Any ideas?
    When you see something with x^2 as the largest power or in any case where you may complete the square e.g  x^4+2x^2+3=(x^2+1)^2+2 . Then you want use a trig substitution. A trig substition involves a squared term and a constant. This is useful when the whole term is bracketed by a power which makes the normal integration complex.

    For your question
    \int \sqrt{5+4x-x^2} = \int \sqrt{9-(x-2)^2}
    let   x-2=\frac{sinx}{3}
    And the rest is just a normal substitution

    Also there are 3 different trig substitutions sin, tan and sec. see if you can tell when to use each one as each one of them have a specific time and place to be used.
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