Hello,
I was trying to integrate a not to complicate function, but the result
was very strange.
(%i161) ff:exp(-x^2/3^2)*sin(x)^2*cos(2*x);
(%o162) %e^(-x^2/9)*sin(x)^2*cos(2*x)
(%i163) quad_qag(ff,x,-4*%pi,4*%pi,6);
(%o163) [-1.329012281002591,1.8823701278258831*10^-14,183,0]
(%i164) integrate(ff,x,-4*%pi,4*%pi);
(%o164) -(%e^(-36)*sqrt(%pi)*(3*erf((4*%pi+18*%i)/3)-6*%e^27*erf((4*%pi
+9*%i)/3)-6*%e^27*erf((4*%pi-9*%i)/3)+3*erf((4*%pi-18*%i)/3)+6*%
e^36*erf((4*%pi)/3)))/8
(%i165) float(%);
(%o165) -5.1390589659105944*10^-17*(3.0*erf(0.33333333333333*(18.0*%i
+12.56637061435917))-3.192289443610792*10^+12*
erf(0.33333333333333*(9.0*%i+12.56637061435917))-3.192289443610792*10^
+12*erf(0.33333333333333*(12.56637061435917-9.0*%i))+3.0*
erf(0.33333333333333*(12.56637061435917-18.0*%i))+2.5867389201337716*10^
+16)
The result of the numerical integration seems correct, but the symbolic
result is quite strange. Especially if one increases the divident (9) in
the exponential function integrate results in 0
(%i171) ff:exp(-x^2/50^2)*sin(x)^2*cos(2*x);
(%o171) %e^(-x^2/2500)*sin(x)^2*cos(2*x)
(%i172) integrate(ff,x,-4*%pi,4*%pi);
(%o172) -
(%e^(-10000)*sqrt(%pi)*(25*erf((2*%pi+2500*%i)/25)-50*%e^7500*erf((2*%pi
+1250*%i)/25)-50*%e^7500*erf((2*%pi-1250*%i)/25)+25*erf((2*%pi-2500*%
i)/25)+50*%e^10000*erf((2*%pi)/25)))/4
(%i173) float(%);
(%o173) 0.0
while the correct result should be close to
(%i169) ff:sin(x)^2*cos(2*x);
(%o169) sin(x)^2*cos(2*x)
(%i170) integrate(ff,x,-4*%pi,4*%pi);
(%o170) -2*%pi
if I did not make a simple mistake.
Any help?
Thanks a lot,
Detlef