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

Calculus help another one

  1. Oct 9, 2003 #1
    Calculus help plz!!! another one

    Can someone plz show me how to show that this problem below is CORRECT? Thanks a lot.
    Integral of dx/(1-x^2) = x/(1-x)
     
  2. jcsd
  3. Oct 9, 2003 #2
    Use the substitution x=sinu.
     
  4. Oct 9, 2003 #3
    Re: Calculus help plz!!! another one

    Hello, gigi9!

    The answer is not correct . . .

    We can use Partial Fractions: 1/(1 - x^2) = A/(1 - x) + B/(1 + x)
    and find that: A = 1/2, B = -1/2.

    The answer will be: (1/2) ln|(1 - x)/(1 + x)| + C
     
  5. Oct 9, 2003 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The easiest way to check if an integral is correct is to invert the operation and differentiate.

    Via the fundamental theorem of calculus, if

    ∫ dx / (1 - x^2) = x / (1 - x)

    then

    1 / (1 - x^2) = (d/dx) (x / (1 - x))

    So if we actually perform the differentiation, we get:

    1 / (1 - x^2) = 1 / (1 - x)^2

    Because this equation is false, the original problem (as you've written it) must be false as well.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Calculus help another one
  1. Calculus help (Replies: 3)

  2. Calculus help (Replies: 2)

  3. Calculus help (Replies: 11)

Loading...