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Integration by substitution

  1. Oct 22, 2006 #1
    Hello,

    evaluate the following integral:

    [tex]\int x \sqrt{x^2+a^2}dx [/tex]

    definite integral from 0 to a

    what I did was

    u = x^2 + a^2
    du = 2xdx

    1/2 sqrt(u)du

    I just dropped the a^2 because we were finding the derivative of x but feel that it's very wrong.


    Any suggestions are much appreciated.

    thanks.
     
    Last edited: Oct 22, 2006
  2. jcsd
  3. Oct 22, 2006 #2

    radou

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    It's correct, if a is a constant.
     
  4. Oct 22, 2006 #3

    arildno

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    Why do you feel it is wrong?
    Ask yourself:
    1. What is the derivative of a constant?

    2. What are the corresponding u-limits compared to the given x-limits?
     
  5. Oct 22, 2006 #4

    Office_Shredder

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    You'll notice that when you go from u to x again, the a2 term pops back in.

    So it's not like you completely lost it
     
  6. Oct 22, 2006 #5
    hey,

    thanks again for all the help. I learn so much from this website and it helps me be much more confident with the problems.

    d/dx of C = 0

    and the corresponing u limits are 0 + a^2 and a^2 + a^2

    what throws me off about dropping the a^2 is that a itself is one of the limits of integration.

    thanks!
     
  7. Oct 22, 2006 #6

    arildno

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    Why should that matter??
    Would you have accepted it if the limit was some number c instead?
     
  8. Oct 22, 2006 #7
    ah ok, I understand now. thanks again.
     
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