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!

Confusing Integration Question?

  1. Aug 5, 2012 #1
    Confusing Integration Question??

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

    The question is as attached.



    3. The attempt at a solution

    I am very confused by the question. Firstly is I(y) a function like (tan-1y) or an operator like ∫y?

    Then they say I(y) - I(∞) = (∏/2) - tan-1y so I suppose that I(y) is basically just -tan-1y.


    I(y) - I(∞) = (∏/2) - tan-1y

    lim(y→0) [ I(y) - I(∞) ] = (∏/2) - 0 = (∏/2)

    But returning to the question, as you let y→0, all you get is

    y(0) = ∫ sinx /x dx = tan-10 = 0

    But that doesn't look right at all.


    I hope someone can clear up all the terminology they are using...
     

    Attached Files:

  2. jcsd
  3. Aug 5, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Re: Confusing Integration Question??

    The terminology is very clear: I(y) is a function of y, given by a formula in the picture.

    RGV
     
  4. Aug 5, 2012 #3
    Re: Confusing Integration Question??

    But when they take the limit of y->0, all you get is I(0) = ∫ sinx /x dx = tan-10 = 0


    When you take the limit of y-> ∞, all you get is I(∞) = 0 (If you substitute ∞ into the question)
     
    Last edited: Aug 5, 2012
  5. Aug 5, 2012 #4
    Re: Confusing Integration Question??

    They say very plainly that [itex]I(\infty) = 0[/itex], so [itex]I(y) = \frac {\pi} {2} - tan^{-1}(y)[/itex], including [itex]y = 0[/itex].
     
  6. Aug 5, 2012 #5
    Re: Confusing Integration Question??

    Oh I think I got it now! Cause when you integrate ∂/∂y = - 1/(1+y2) you get

    I(y) = -tan-1y + C

    Based on the first equation, we know y(∞) but not y(0).

    I(∞) = 0, so you solve C = ∏/2...


    Everything makes sense now, thank you!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Confusing Integration Question?
  1. Confusing Question (Replies: 4)

  2. Confusing integral! (Replies: 3)

  3. Confusing Integral! (Replies: 8)

Loading...