Thanks for the report. Sage symbolic integration has indeed a lot of problems! Note that it integrates cleanly the first integral
sage: f = integral(r*sqrt(4-r^2), (r,0,s)) sage: f 1/3*(s^2 - 4)*sqrt(-s^2 + 4) + 8/3 That you can even check numerical values (this numerical integration works very well thanks to GSL) ​sage: numerical_integral(r*sqrt(4-r^2), 0, 0.5) (0.24605207528703113, 2.731726792404644e-15) sage: f.subs(s=0.5) 0.246052075287031 sage: numerical_integral(r*sqrt(4-r^2), 0, 1.0) (0.9346158590977892, 1.0376320459501866e-14) sage: f.subs(s=1.0) 0.934615859097789 Then as you already noticed one obtains the very wrong sage: g = f.subs(s=1+cos(t)) sage: integral(g, (t,0,2*pi)) 16/3*pi whereas the expected value should be around sage: numerical_integral(g, 0, 2*pi) (7.299499510756003, 8.10407242508138e-14) which is indeed close to maple symbolic answer sage: expr = -34/9*sqrt(2) - 7/3*log(3+2*sqrt(2)) + 16/3*pi sage: expr.n() 7.29949951075600 Vincent -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
