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Homework Help: Finding F(1) and F'(1)

  1. May 12, 2005 #1
    Ok i have another problemo here...

    if [tex] F(x) = \int_{-x}^{x} \frac{dt}{1+t^2}[/tex]

    Find F(1) and F'(1)....I need some assistance...the anti derivative is

    [tex] arctan(t) [/tex] so then.... do i set that equal to f(1) and solve for t? and then for F', take the derivative and then solve for t again? im kind of confused... :confused:
     
  2. jcsd
  3. May 12, 2005 #2

    OlderDan

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    You can do the integral to get F(x) for all x in the domain of F. Then take the derivative with respect to x to get F'(x). Evaluate both at x = 1. You can also find F'(x) using the fundamental theorem of calculus. For the latter approach, you might want the break the integral into two intervals at any constant a such that -x<a<x. a = 0 would be a convenient choice, but any constant value will do.
     
  4. May 12, 2005 #3
    ok i got it ..thank you.
     
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