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Integral Evaluation

  1. Jul 31, 2007 #1
    1. The problem statement, all variables and given/known data
    How would you evaluate

    [tex] \frac{d}{dx} \int _{x}^{tanx}exp(-t^2)dt[/tex] ?


    2. Relevant equations



    3. The attempt at a solution

    So I think you want to substitute variables int order to get the lower limit a constant and the upper limit a variable with constant derivative. Then we just take out the derivative operator and the integral sign. I just cannot think of the right substitution...
     
    Last edited: Jul 31, 2007
  2. jcsd
  3. Jul 31, 2007 #2

    bel

    User Avatar

    let [tex]\int exp(-t^2)dt = F(t) [/tex],

    then, [tex]\int _{x}^{tanx}exp(-t^2)dt =
    F(tanx)-F(x) [/tex]

    then use the chain rule to differentiate, since you already know the derivative of [tex] F(x)[/tex].
     
  4. Jul 31, 2007 #3
    That works. Thanks.
     
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