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Integration Question I have a midterm in 45 mins AH!

  1. Jan 24, 2007 #1
    Integration Question.. I have a midterm in 45 mins!! AH!

    1. The problem statement, all variables and given/known data

    integral with bounds [5,x^2] of f(t)dt = (5x^2)/(x^4+6) + C

    f(t) = ?
    C = ?
    2. Relevant equations

    Uhm.. I don't know. Im guessing you have to use the FTC.

    3. The attempt at a solution

    I've have tried so many different types of substitution and stuff with no luck. I really have no idea what method is required to solve this; I dont remember learning it.
  2. jcsd
  3. Jan 24, 2007 #2
    Probably way beyond me but have you tried partial fractions? And substitution?

    Can you show what you've tried?
    Last edited: Jan 24, 2007
  4. Jan 24, 2007 #3


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    The FTC says that

    [tex]\int_a^b f(t)dt = F(b)-F(a)[/tex]

    where F'(t)=f(t).

    So you want to find which function F(t) is such that F(x²) = -(5x^2)/(x^4+6). Then differentiate it to get f(t). About C, well C=F(5), so once you get F(t), finding C is a formality.
  5. Jan 24, 2007 #4


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    Yes, the derivative of [tex]\int_a^x f(t)dt[/itex] is f(x). But you are given [itex]\int_a^{x^2} f(t)dt[/itex]. Let u= x2 and use the chain rule: [itex]\frac{df}{dx}= \frac{df}{du}\frac{du}{dx}[/itex].

    To determine C, let x= some convenient value and evaluate.
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