1. Limited time only! Sign up for a free 30min personal 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!

Partial fractions pronblem help

  1. Apr 9, 2009 #1
    1. The problem statement, all variables and given/known data
    F(X)=[tex]\int[/\frac{1}{1+t^3}


    2. Relevant equations



    3. The attempt at a solution
    I have tried different substitutions to find fog where g(t) = ? But am getting stuck
     
  2. jcsd
  3. Apr 9, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Antiderivative

    1+t^3 can be factored. Start by using partial fractions.
     
  4. Apr 9, 2009 #3
    Re: Antiderivative

    I tried partial fractions but I landed up with A/(1+t) + B/(1-t+t^2). Cannot find values for A & B that work.
     
  5. Apr 9, 2009 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Antiderivative

    Try A/(1+t)+(B*t+C)/(1-t+t^2). If you have a quadratic in the denominator it's not necessarily a constant in the numerator.
     
  6. Apr 9, 2009 #5
    Re: Antiderivative

    I got the problem wrong.
    F(x)=Integ (1+t^3)^-1 from 0 to x^2. Find F'(x)

    How do I proceed
     
  7. Apr 9, 2009 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Antiderivative

    That makes your job a lot easier. Look up the Fundamental Theorem of Calculus and the Leibniz integral rule. What's the derivative of an integral?
     
  8. Apr 9, 2009 #7
    Re: Antiderivative

    The derivative of an integral is the function itself if it is continuous over the specified region. In this case, the function is not continuous at t=-1, But that is not in 0 to x^2.

    I don't know how Leibniz rule works here
     
  9. Apr 9, 2009 #8
    Re: Antiderivative

    Ok.
    F'(x)=d/dx(integ f(t)) over 0 to x^2. = f(x).2x=(1/1+x^6).2x
     
  10. Apr 9, 2009 #9

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Antiderivative

    That's not good. Yes, the integral of a function from 0 to x of f(t) is f(x). If the upper limit is not x but some function of x (like x^2) you have to use the chain rule to find d/dx. That's what the Leibniz thing is about.
     
  11. Apr 9, 2009 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Antiderivative

    Ok, you got it. Good work.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Partial fractions pronblem help
  1. PARTIAL FRACTION Help! (Replies: 9)

Loading...