1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fundamental Theorem

  1. Jul 13, 2008 #1
    The problem statement, all variables and given/known data
    Question One:
    Find a continuous function f and a number a such that

    [tex]2 + \int_{a}^{x} \frac {f(t)} {t^{6}} \,dt = 6 x^{-1}[/tex]

    Question Two:
    At what value of x does the local max of f(x) occur?
    [tex]f(x) = \int_0^x \frac{ t^2 - 25 }{ 1+\cos^2(t)} dt[/tex]

    The attempt at a solution
    I just need some pointers of where to get started.
    Question One:

    So I used FTC1 on both sides,

    [tex]2 + f(x) / x^{6} = 6x^{-1}[/tex]

    [tex]f(x)= 6x^{5} - 2[/tex]

    I'm not sure how to find a, evaluation theorem?

    Question Two:
     
    Last edited: Jul 13, 2008
  2. jcsd
  3. Jul 13, 2008 #2
    I don't know about an analytic solution, but the second part of the problem is very feasible numerically. You can solve in Mathematica in only a few lines by turning it into a minimization problem.
     
  4. Jul 13, 2008 #3
    Well, for Question one:

    Can anyone confirm that [tex]f(x) = 6x^{5}[/tex] and a = 2.

    I'm pretty sure that a = 2 since,

    F(x) - F(a) = [ [tex]6x^{5} / x^{6}[/tex] ] - [ 2 ] = [tex]6x^{-1} - 2[/tex]
     
  5. Jul 13, 2008 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    How does the FTC just let you drop an integral sign out like that? (In 1.)
     
  6. Jul 14, 2008 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, that is not correct. You have differentiated the left side of the equation but not the right.

    Once you have found the function, put it into the integeral.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fundamental Theorem
  1. Fundamental Theorem? (Replies: 7)

Loading...