Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By HallsofIvy

Math Help - Fundmental Theorem of Calculus problem #2

  1. #1
    Junior Member
    Joined
    Sep 2013
    From
    UK
    Posts
    28
    Thanks
    1

    Fundmental Theorem of Calculus problem #2

    The question is: The function f is differentiable on (−∞, ∞). Determine f (2) in the following cases:

    \int_0^{f(x)}{t^2}dx={x^2}{(1+x)}}

    So I let {u}={f(x)} ==> \int_0^u{t^2}{dt} ==>
    \frac{d}{du} \int_0^u{t^2}{dt}={(f(u))^2}

    So \frac{d}{dx} \int_0^u {t^2}{dt}={(f(u))^2} \frac{du}{dx} ==> {(f(x))^2}{f'(x)}={2x}+{3x^2}

    Assuming that my steps are correct (and I'm not certain that they are), where do I go from here? For instance, what is {f'(x)}?

    Many thanks for any suggestions for this problem!
    CP


    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,427
    Thanks
    1857

    Re: Fundmental Theorem of Calculus problem #2

    First, I suspect there is a typo in your statement of the problem. Your integrand is [tex]x^2[tex] but the integral with respect to x!
    I suspect you meant \int_0^{x^2} t^2 dt. Is that correct? Assuming it is-

    I'm not sure why you would differentiate. If you just go ahead and integrate \int t^2 dt= \frac{1}{3}t^3+ C so that \int_0^{f(x)} t^2 dt= \frac{1}{3} (f(x))^3.

    So your equation is \frac{1}{3}(f(x))^3= x^2(1+ x)

    Solve that for f(x). (f(x) is just a number. This is exactly the same as solving \frac{1}{3}y^3= x^2(1+ x) for x.)
    Thanks from CrispyPlanet
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. another book about fundmental theorem of algebra problem...
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: July 15th 2011, 04:03 PM
  2. Fundmental Group
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 9th 2010, 08:13 PM
  3. Replies: 7
    Last Post: December 10th 2009, 01:18 PM
  4. fundamental theorem of calculus problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 30th 2009, 03:37 PM
  5. Replies: 3
    Last Post: November 17th 2008, 05:03 PM

Search Tags


/mathhelpforum @mathhelpforum