Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrating 2nd order derivative

  1. Aug 22, 2009 #1
    The question is

    If f(x) = 7x^3 + 8x^2 - x + 11, evaluate :

    a, Integral +1 - -1 f(x) dx
    b, Integral +1 - -1 f'(x) dx
    c, Integral +1 - -1 f''(x) dx

    For a, Just integrate each individual and then input the figures which gave me

    1.75x^4 + (8x^3)/3 - 0.5x^2 + 11x

    Which when I input the figures gives me 27 1/3.

    It is b, which I am unsure about. Do I intergrate 1.75x^4 + (8x^3)/3 - 0.5x^2 + 11x and then put the values in?

    Some guidence would be most appreciated, thank you.
     
  2. jcsd
  3. Aug 22, 2009 #2

    Gib Z

    User Avatar
    Homework Helper

    Hello Maths Muppet! Welcome to PF.

    Are you familiar with the fundamental theorem of Calculus? The form of it that is useful here is:

    [tex]\int^b_a g'(x) dx = g(b) - g(a)[/tex]

    You can apply that to b and c quite directly.
     
  4. Aug 24, 2009 #3
    I think your reply has just confused me a little bit. I might be using the wrong termonology but I thought all that I would have to is integrate 1.75x^4 + 8x^3 - 0.5x^2 + 11x and then insert the values back in. Is this correct?
     
  5. Aug 24, 2009 #4

    rock.freak667

    User Avatar
    Homework Helper

    f'(x) means the derivative of f(x) with respect to x. Integration is the reverse of differentiation. So for example, if f(x)=x2, then f'(x)=2x. So ∫2x dx=x2+C.

    See now why Gib Z said you can directly work out the integral?
     
  6. Aug 25, 2009 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    1.75x^4+ 8x^3- 0.5 x^2+ 11x is the integral of your original function and does not have to be integrated again for problem (a).

    Gib_z's point is that
    [tex]\int_{-1}^1 f'(x)dx= f(1)- f(-1)[/tex]
    and that
    [tex]\int_{-1}^1 f"(x)dx= f'(1)- f'(-1)[/tex]
     
  7. Aug 28, 2009 #6
    [itex]\int_a^b f(x)\,dx\,=\,F(b)\,-\,F(a),\,where\,F'(x)\,=\,f(x).[/itex]
    FTOC is great!!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integrating 2nd order derivative
  1. 2nd derivative rule (Replies: 4)

Loading...