Getting Natural With Pi (Posted on 2007-11-27)

       y
     ∫(ex - 1)-0.5 dx = pi/6 
      ln(4/3)

	Submitted by K Sengupta
Rating: 3.0000 (2 votes)
Solution:	(Hide)
Let √(ex -1) = q Then,   y    ∫ (ex -1)-0.5 dx ln(4/3) = 2*I, where: I = √(e^y - 1)     ∫  (1 + q^2)-1 dq 1/√3 = arc tan √(e^y -1) – pi/6 Accordingly, 2(arc tan √(e^y -1) – pi/6) = pi/6, giving: arc tan √(e^y -1) = pi/4, so that: e^y - 1 = 1, giving: e^y = 2, so that: y = ln(2)

	Subject	Author	Date
	re(4): True, there is only one solution.	Kurious	2007-11-29 07:07:16
	re(3): There are two solutions	Charlie	2007-11-28 09:23:19
	re(2): There are two solutions	Kurious	2007-11-28 07:28:10
	re: There are two solutions	Charlie	2007-11-27 21:53:38
	There are two solutions	Kurious	2007-11-27 18:54:23
	Switch to other integral!	Chesca Ciprian	2007-11-27 14:34:19
	analytical solution	Daniel	2007-11-27 13:51:46
	numerical solution -- spoiler	Charlie	2007-11-27 10:43:27