this report came in from the "report a problem" link for 4.1.1. -------------------------
Sage gives an incorrect value when calculating a definite integral analytically: sage: integrate(cos(x)^2 * (1 + sin(x)^2)^-3,x,0,pi/2) 21/64*pi*sqrt(2) sage: _.n() 1.45782096408321 The correct answer is 7/64*pi*sqrt(2) = 0.48594. Sage gets this when doing the integral numerically, or when going not quite to pi/2: sage: numerical_integral(cos(x)^2 * (1 + sin(x)^2)^-3,0,pi/2) (0.48594032136107129, 5.3950213336880916e-15) sage: integrate(cos(x)^2 * (1 + sin(x)^2)^-3,x,0,pi/2-0.0001).n() 0.485940321361 The integrand is perfectly well-behaved at pi/2. The problem may be related to the fact that the indefinite integral contains a term like arctan(sqrt(2)*tan(x)), which is ill-defined at x=pi/2. ------------------------- Harald --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
