Hi Sergio
Since the primitive of
exp(x^2)*x^2
is
Ly=x*exp(x^2)/2-.5*1j*(pi)^.4/2*erf(1j*x)
then the integral in the interval [y1 y2] is
L=Ly2-Ly1
this is
y2=4;
Ly2=y2*exp(y2^2)/2-.5*1j*(pi)^.5*erf(sym(1j*y2))
Ly2 =
149084195602433/8388608 - (erf(4i)*3991211251234741i)/4503599627370496
y1=-4;
Ly1=y1*exp(y1^2)/2-.5*1j*(pi)^.5*erf(sym(1j*y1))
Ly1 =
(erf(4i)*3991211251234741i)/4503599627370496 - 149084195602433/8388608
the value of the integral is
L= Ly2-Ly1
L =
149084195602433/4194304 - (erf(4i)*3991211251234741i)/2251799813685248
way around erf() only working for real inputs
L= double(Ly2-Ly1)
L =
3.7843e+07
therefore
C=1-L
C =
-3.7843e+07
Repeating with
format double
the result is
L =
3.784324335121135e+07
Comment:
When attempting direct integration with command sum
x=[-4:.001:4];L=sum(exp(x.^2) .* x.^2)
L =
3.4537e+10
x=[-4:.00001:4];L=sum(exp(x.^2) .* x.^2)
L =
3.4396e+12
x=[-4:.0000001:4];L=sum(exp(x.^2) .* x.^2)
L =
3.4395e+14
The slopes when approaching -4 and 4 are too sharp for command sum.
Grazie tante per la sua attenzione.
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thanks in advance
John BG
