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Definition of derivative integration problem

  1. Jan 13, 2004 #1
    This was an extra credit problem on our last test. We haven't learned how to do it yet but I was just curious as to how it would be done.

    [tex]\int^{x^2}_{5} \sqrt{1 + t^2} \,dt = G(x) [/tex]
    Find G'(x).
  2. jcsd
  3. Jan 13, 2004 #2


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    Try going back to the definition of derivative.
  4. Jan 14, 2004 #3
    The formula is
    [tex]\int_{f(x)}^{g(x)} \phi (x)dx=\phi [g(x)]g'(x) - \phi [f(x)]f'(x)[/tex]
  5. Jan 14, 2004 #4


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    himanshu121, that's an unfortunate notation. It's difficult to distinguish where x is the "dummy" variable and where it is the final variable.

    Better would be:
    [tex]\int_{f(x)}^{g(x)} \phi (t)dt=\phi [g(x)]g'(x) - \phi [f(x)]f'(x)[/tex]
  6. Jan 14, 2004 #5
    Oh Yes Thanks Halls for correcting
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