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How to find the integral of e^(sqrt(x)) as x goes from 0 to 1

  1. Dec 20, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex]\int_0^1 e ^(sqrt. x) dx [/tex]

    2. Relevant equations

    3. The attempt at a solution

    i don´t know what to let u equal to... maybe sqrt.x? but what good would that do when u is differentiated?
  2. jcsd
  3. Dec 20, 2007 #2
    hmm, your latek messed up

    [tex]\int_{0}^{1} e^{\sqrt{x}}dx[/tex]

  4. Dec 20, 2007 #3
    yes, thanks... i´m still figuring out how to use it :smile:
  5. Dec 20, 2007 #4
    Let u=[tex]\sqrt{x}[/tex]

    then, use another "simple" substitution so that you only have 1 variable.

    then, you will need to use integration by parts.
  6. Dec 20, 2007 #5
    i still haven´t figured the problem itself though...
  7. Dec 20, 2007 #6
    shoot, at least you've already almost got it down. there are ppl with like 500+ posts and still don't use latek, hurts my eyes :p
  8. Dec 20, 2007 #7
    that was before learning integration by parts so i guess i´m not supposed to use it
  9. Dec 20, 2007 #8
    what technique are you not allowed to use?
  10. Dec 20, 2007 #9
    integration by parts... thats why i´m stuck
  11. Dec 20, 2007 #10
    there's no way around this problem without the use of integration by parts, want to work this problem together by use of parts?
  12. Dec 20, 2007 #11
    do i let u = [tex]e^\sqrt{x}[/tex] ?
  13. Dec 20, 2007 #12
    the derivative of your substitution would then become



    messy. then you will need to take the ln of your u-substitution so you can get your problem in terms of 1 variable.
    Last edited: Dec 20, 2007
  14. Dec 20, 2007 #13
    so then u is just [tex]\sqrt{x}[/tex] ?
  15. Dec 20, 2007 #14
    yes and i can help you through integration by parts, b/c we can't integrate this problem by simple substitutions.
  16. Dec 20, 2007 #15
    ok... u = [tex]\sqrt{x}[/tex]
    and du = [tex]du=\frac{1}{2\sqrt{x}}dx[/tex]
  17. Dec 20, 2007 #16
    what would dv be?
  18. Dec 20, 2007 #17
    well first, let's make it a "t-substitution" b/c we'll need to use U and V for parts.



    now we need our integration in terms of 1 variable, so



    [tex]\int e^{\sqrt{x}}dx \rightarrow 2\int te^{t}dt[/tex]

    now we do integration by parts.
    Last edited: Dec 20, 2007
  19. Dec 20, 2007 #18
    no, the last step was a simple substitution ... this next step we will use parts.
  20. Dec 20, 2007 #19
    wait.. i´m confused... now i have [tex]\sqrt{x}[/tex] as u
    and then i have to square it?
    Last edited: Dec 20, 2007
  21. Dec 20, 2007 #20
    [tex]2\int te^{t}dt[/tex]

    [tex]\begin{array}{cc}u=t & dV=e^{t}dt \\ du=dt & V=e^{t}\end{array}[/tex]

    i'm sure you can take it from here! (judging from your other post)
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