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F(x) = integral from x to x^2

  1. May 30, 2009 #1
    1. The problem statement, all variables and given/known data

    f(x) = integral from x to x^2

    t^2 dt

    find f ' (x) = ?
    find f '(5)= ?

    2. Relevant equations



    3. The attempt at a solution

    Break the integral in 2: \int_x^{x^2} t^2 dt = \int_x^{0} t^2 dt +\int_0^{x^2} t^2 dt = -\int_0^{x} t^2 dt + \int_0^{x^2} t^2 dt
    Then take the derivative of both integrals using the FTC.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 30, 2009 #2
    Re: integral

    You don't even need to integrate the expression if you already learned the fundamental theorem of calculus (just be careful with your variables!). Where are you having difficulty?
     
  4. May 30, 2009 #3
    Re: integral

    This was my ans and it says that it is wrong
    f ' (x) = -x^3/3+x^6/3

    f ' ( 5 ) = 5166.666667

    i also put

    f ' ( x) = -x^2 + x ^ 4 and that was also wrong
     
  5. May 30, 2009 #4

    djeitnstine

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    Gold Member

    Re: integral

    What are you using that says it is wrong? Is it a book? A program? Because sometimes a program requires input a special way.
     
  6. May 30, 2009 #5
    Re: integral

    it is a program online i put the top ans on the program right but it says that both are incorrect ans for the f'(x) and f'(5)
     
  7. May 30, 2009 #6

    djeitnstine

    User Avatar
    Gold Member

    Re: integral

    Figures, try putting your answer in different forms.

    Such as (x^6)/3-(x^3)/3

    and 5166.7

    etc... I don't know exactly what they want, but you should experiment to see what format they accept.
     
  8. May 30, 2009 #7

    Cyosis

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    Homework Helper

    Re: integral

    This is not true, f(x) is defined as [itex]f(x)=\int_x^{x^2} t^2 dt=-x^3/3+x^6/3[/itex]. Now the ' means that you have to differentiate to x.
     
  9. May 30, 2009 #8

    djeitnstine

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    Gold Member

    Re: integral

    good looking I didn't even see the '
     
  10. May 30, 2009 #9
    Re: integral

    That is indeed incorrect. You are giving f(x), while the question asks for f'(x). Once again, note that there is no need to integrate the expression. Use the fundamental theorem of calculus.
     
  11. May 30, 2009 #10
    Re: integral

    thanks alot guys i figured it out
     
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