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Integration using a TI-89 produces wrong value?

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  1. Aug 24, 2013 #1
    Hi Physics Forum,

    I've just started taking Diff EQ and have been using my calculator for most integrations. I've come across two problems that I hope have answers.

    1) When I try the integral of (x+1) (the quantity! not just x+1), my calculator still spits out (x^2/2)+x while the real answer should be (-(x+1)^2)/2. Is there a way to make my calculator identify (x+1) as the quantity (or is it factor? I forgot the actual term) rather than just x+1?

    2) When I integrate 3/(100+2*x) I'm getting 3/2 * ln(x+50). However, I'm 99% sure the answer should be 3/2 * ln(100+2x). What am I/the calculator doing wrong?

    Any and all answers are appreciated, thanks so much!
     
  2. jcsd
  3. Aug 24, 2013 #2

    Borek

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    Staff: Mentor

    [tex]\frac 3 {100+2x} = \frac 3 {2(50+x)}[/tex]
     
  4. Aug 24, 2013 #3
    This is where I'm confused. Multiple integral tables say that that

    the integral of 1/(ax+c) is (1/a) * ln(ax+c). This would yield 3/2 * ln(100+2*x) where as the integral of your answer would yield 3/2 * ln(50+x). So I'm left with two different answers to choose from.

    Either 3/2 * ln(100+2*x) or 3/2 * ln(50+x). Very curious =x
     
  5. Aug 24, 2013 #4

    AlephZero

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    Science Advisor
    Homework Helper

    In both your examples, the difference in the "answers" is just a constant, so you can think of it as part of the arbitrary constant in an indefinite integral.

    If you are going to evaluate a definite integral, the arbitrary constant cancels out so it doesn't matter.

    In the first example the difference is the constant 1/2.

    In the second example, from the properties of logarithms,
    log(100 +2x) = log(2(50 + x)) = log(50+x) + log 2.
     
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