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Fund. Theorem Calc. Part I

  1. Sep 19, 2006 #1
    Suppse the following function was written:

    [tex]
    f(x)=\int_{0}^{x} \frac{t-1}{t^4+1} dt
    [/tex]

    Then we could assume there is a solution:
    f(x) = F(x) - F(0)

    Take the derivative:
    f'(x) = F'(x) - F'(0) = F'(x)
    [tex]
    f'(x)=\frac{x-1}{x^4+1}
    [/tex]

    Then we could determine if the function is increasing or decreasing over an interval. Without taking the antiderivative how could we determine what the following values are:
    f(0)
    f(1)
    f(-1)
     
  2. jcsd
  3. Sep 19, 2006 #2

    radou

    User Avatar
    Homework Helper

    F(x0) represents the value of the primitive function F at a point x0, not a function. Do not mess up variables x with fixed points, which are conventionally called x0, a, b, c, etc.
     
  4. Sep 19, 2006 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    f(0) is easy:
    [tex]F(0)= \int_0^0 \frac{t-1}{t^4-1}dx= 0[/tex]
    There is no way to determine f(1) or f(-1) without actually doing the integral.
     
  5. Sep 19, 2006 #4
    Thank you for your help.
     
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