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!

Simple definite integral

  1. May 26, 2010 #1
    1. The problem statement, all variables and given/known data

    What is wrong with the equation:

    [tex]\int^{\pi}_{0} sec^{2} x dx = tan x\right|^{\pi}_{0} = 0[/tex]

    2. Relevant equations

    None

    3. The attempt at a solution

    I don't know where to begin. I am inclined to give a mathematical (as opposed to a paragraph-like) explanation as to why this is incorrect. Clearly because of the vertical asymptotes of the integrand, the area under the curve on that interval will be infinite. But I know that this will not suffice as an answer, so how do show this mathematically or perhaps be more specific? Or both an explanation and mathematical explanation.

    Thank you in advance!
     
  2. jcsd
  3. May 26, 2010 #2
    I am not sure if its the correct method but I hope it helps.

    1st evaluate its limit b/w the interval 0 to Pi/2. Then Calculate it from Pi/2 to Pi. The total area has to be the sum of them which will be equal to infinity :D.
     
  4. May 26, 2010 #3
    The Fundamental Theorem of Calculus applies only when both the integrand and it's antiderivative are analytic in the domain of integration. Is that the case here?

    Also, this looks nicer:

    [itex]tan(x)\biggr|_a^b[/itex]
     
  5. May 27, 2010 #4
    alright, so we cannot apply the FTC in this case, at least in this form.

    Is it possible to break it down into two integrals, from zero to pi/2, and then pi/2 to pi? As nuketrooper suggested?

    Though tan(pi/2) approaches infinity...so we can't really apply the FTC there either. Is there a way of manipulating or correcting this formula so we CAN compute the integral?

    Thank you in advance!
     
  6. May 27, 2010 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [tex]\int_0^\pi sec^2(x) dx= \lim_{\alpha\to \pi/2^-}\int_0^\alpha sec^2(x)dx+ \lim_{\beta\to \pi/2^+}\int_\beta^\pi sec^2(x)dx[/tex].

    Of course, those limits might not exist.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple definite integral
  1. Definite integral (Replies: 6)

Loading...