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Definite integral

  1. Jan 17, 2015 #1
    1. The problem statement, all variables and given/known data
    There is a problem in physics. i need to calculate the definite integral:
    $$y=\int^{10}_2 \frac{13.2}{x^{1.4}}$$

    2. Relevant equations
    $$\int x^{-a}=\frac{1}{-a+1}x^{-a+1}$$

    3. The attempt at a solution
    $$y=\int^{10}_2 \frac{13.2}{x^{1.4}}=13.2\int^{10}_2 x^{-1.4}=13.2 \frac{1}{-0.4}x^{-0.4}|^{10}_2=-0.63$$
    According to a graph i made with a graph software it came out -11.9, see picture
     

    Attached Files:

  2. jcsd
  3. Jan 17, 2015 #2

    Orodruin

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    Neither of these answers can be correct, you have the integral of a positive quantity and the result must be positive. I suggest rechecking your arithmetics.

    You really should also consider always writing out the dx in the integral for clarity. The expressions are mathematically incomplete without it.
     
  4. Jan 17, 2015 #3
    $$y=\int^{10}_2 \frac{13.2}{x^{1.4}}dx=13.2\int^{10}_2 x^{-1.4}dx=$$
    $$=13.2 \frac{1}{-0.4}x^{-0.4}|^{10}_2=-33\left(\frac{1}{10^{0.4}}-\frac{1}{2^{0.4}}\right)=11.9$$
     
  5. Jan 17, 2015 #4

    Orodruin

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    That looks much better and is correct as far as I can tell.
     
  6. Jan 17, 2015 #5
    Thanks
     
  7. Jan 17, 2015 #6

    Ray Vickson

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    Please recognize that 11.9 is an approximation to the true answer (obtained by rounding to 3 significant figures); when you write "=11.9" you are hiding that fundamental fact, and are writing something that is not true. I think it is important that you broadcast your understanding of that issue by saying so explicitly---for example, by saying " ... = 11.9, rounded to 3 digits" or something similar. Even better would be to write "... ≈ 11.9 ..." or "... ##\doteq## 11.9 ...".
     
  8. Jan 17, 2015 #7
    Right, i will use that notation next times, thanks
     
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