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Find the derivative of an integral!

  1. Apr 18, 2010 #1
    [tex]\frac {d} {dt}\int_{1}^{x} sint dt[/tex]
     
  2. jcsd
  3. Apr 18, 2010 #2

    Char. Limit

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    Gold Member

    This one is easy if you remember the First Fundamental Theorem of Calculus.
     
  4. Apr 18, 2010 #3
    Thanks, i guess i was just looking for what particular method to use.
     
  5. Apr 18, 2010 #4

    Char. Limit

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    Well, there are two methods...

    You could solve the integral, which isn't too hard (the answer is cos(1)-cos(x)), and then differentiate it wrt x to reveal the function. But it's easier to just remember the FTC.
     
  6. Apr 18, 2010 #5
    The result is zero.
     
  7. Apr 18, 2010 #6
    Are you sure that you notated this correctly? It looks unusual to me. The integration would be done with respect to a variable t (essentially a dummy variable), and the result will be a function of x (the upper limit). The derivative of this with respect to t would then be zero.

    Did you intend the derivative to be with respect to x?
     
  8. Apr 18, 2010 #7
    Yes, sorry, it's d/dx

    Wouldn't the result be just "sinx" ?
     
  9. Apr 18, 2010 #8
    yes.
     
  10. Apr 18, 2010 #9
    Thank you! :)
     
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