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Homework Help: Definite Integral with Absolute Value.

  1. Feb 6, 2014 #1
    The problem is ∫x^2 - 3x - 5 with the lower limit being -4 and the upper limit 7.

    I broke the integrals into three parts from [-4, -1.1926], [-1.1926, 4.1926], [4.1926, 7]

    I did the integral and got (x^3)/3 - (3/2)x^2 - 5x

    I subbed in the lower and upper limits and got 32.861 for [-4, -1.1926], 15.231 for [-1.1926, 4.1926], and finally 28.957 for [4.1926, 7].

    I don't necessarily need a step by step solution ( though it would be greatly appreciated). I would really just like to know if you can spot which/where I am getting the wrong value(s).

    EDIT: The final answer I keep getting is 76.691. The answer I get when I use a definite integral calculator is 83.2233
    Last edited: Feb 6, 2014
  2. jcsd
  3. Feb 6, 2014 #2


    Staff: Mentor

    Is this your integral?
    $$ \int_{-4}^7 |x^2 - 3x - 5|dx$$
    The above is incorrect. You are ignoring the fact that there's an absolute value involved. The key idea is that |a| = a if a ≥ 0, but |a| = -a if a < 0.

    Also, the approximate numbers you use aren't exact, so whatever answer you get will be off some.
    It is against the rules in this forum to provide a complete answer, so a step-by-step solution isn't going to happen.
  4. Feb 6, 2014 #3
    The part you are saying is incorrect was set up by my professor. She put a negative sign in front of the integral for [-1.1926, 4.1926]
  5. Feb 6, 2014 #4


    Staff: Mentor

    Which you didn't mention.

    Anyway, I get 83.2233 as well, so all I can say is that you have an error in one or more of your integrals. Also, as I mentioned already, you should be using the exact numbers for the limits of integration, rather than the decimal approximations. That is, you should be using ##3/2 - \sqrt{29}/2## and ##3/2 + \sqrt{29}/2##, although I suspect that the difference you're getting is caused by an error somewhere else.
  6. Feb 6, 2014 #5


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    Science Advisor
    Homework Helper
    Gold Member

    The two in red are incorrect.
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