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Changing the limits on Integrals

  1. Aug 20, 2011 #1
    I'm confused as to when to change the limits on a definite integral.

    Ex. Integral with the limits a=1, b=5, 3/(x+1)dx

    I set u = x+1 and du = dx

    I used u-substitution and everything worked out fine.

    However for this one....

    Ex. Integral with the limits a = 0, b = 2, 6x^2/sqrt((x^3)-1)

    I used u-substitution u = sqrt((x^3)-1) and so 2du = (6x^2)dx
    However the book says I need to change the limits of the integral.

    So I'm not sure when to change the limits of an integral. Can anyone help? Thanks =D
     
  2. jcsd
  3. Aug 20, 2011 #2
    For the first integral, did you change the integration limits to [2, 6]?

    For the second one, of course you must change the limits of the integral when you make a substitution, but also note that this is an improper integral since the integrand is discontinuous somewhere on [0, 2].
     
  4. Aug 20, 2011 #3
    For the first integral no I did not.
     
  5. Aug 20, 2011 #4

    I like Serena

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    Homework Helper

    Hi kLPantera! :smile:

    You're integrating with respect to x from a to b.
    When you substitute u=u(x) you change the expression to read "du" instead of "dx".
    This means that exactly from this moment on you're integrating with respect to u.
    The limits for u=u(x) are then u(a) and u(b).
     
  6. Aug 20, 2011 #5
    Ah I understand it now lol
     
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