Search results

  1. T

    Improper Integral Proof

    I understand this; what I don't understand is: geometrically why is this true?
  2. T

    Improper Integral Proof

    I understand that if you \lim_{n\rightarrow\infty}\arctan x = \frac{\pi}{2} or \lim_{n\rightarrow-\infty}\arctan x = \frac{-\pi}{2} That's apparent because your ratio of opp./adj. side lengths is growing very quickly as θ approaches π/2. Until, theoretically you have a tiny adjacent side and a...
  3. T

    Improper Integral Proof

    Oops. Sorry, that lower bound is supposed to be -\infty I didn't have the -
  4. T

    Improper Integral Proof

    Hi, I came across this interesting integral \int_{-\infty}^{\infty}\frac{d}{dx}(\arctan x) dx=\pi I can derive the solution analytically, but I cannot think of a geometric proof. Does anyone know geometrically why this integral is equal to pi?
Top