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Evaluating definite integral by substitution

  1. Oct 5, 2012 #1
    1. The problem statement, all variables and given/known data
    By using substitution [tex]u=\frac{1}{t}[/tex], or otherwise, show that

    [itex]\int^∞_1 \frac{t^5}{(1+t^3)^3}dt=\int^1_0 \frac{u^2}{(1+u^3)^3}du[/itex]

    2. Relevant equations



    3. The attempt at a solution
    integral.png

    Well, the reverse can also be done (making t to u). However, I don't know how to change the premise of the integral (from (∞,1) to (1,0). Thank you! I can integrate the integral after that.
     
  2. jcsd
  3. Oct 5, 2012 #2

    SammyS

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    [itex]\displaystyle \lim_{t\,\to\ \ \infty}\frac{1}{t}\ \ =\ \ \underline{\ \ ?\ \ }[/itex]
     
  4. Oct 5, 2012 #3
    0?

    so the integral is just [itex]0- \int\left[\frac{(1/t)^2}{t^2(1+(1/t)^3}\right]^1[/itex]?(sorry don't really know how I'm supposed to write this...)

    and at 0 the integral is 0. but it seems there is something wrong with the sign, because it is negative...
     
    Last edited: Oct 5, 2012
  5. Oct 5, 2012 #4

    SammyS

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    [itex]\displaystyle \int_a^b f(x)\,dx=- \int_b^a f(x)\,dx[/itex]
     
  6. Oct 6, 2012 #5
    oh right! thanks!
     
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