## #635 defint(log(1+exp(A+B*cos(phi))),phi,0,%pi) wrong

closed
nobody
5
2008-11-26
2004-10-26
Anonymous
No

Maxima 5.9.0

C1) assume(B>0,B-A>0)\$
(C2) integrate(log(1+exp(A+B*cos(phi))),phi,0,%pi);
- B B A
(D2) 3 %PI LOG(%E (%E + %E ))

But if we give A and B numerical values

(C3) B:3\$ A:2\$ ev(D2,numer);
(C4)
(C5)
(D5) 2.952421848475173
(C6) B:3.2\$ A:-3\$ ev(D2,numer);
(C7)
(C8)
(D8) .0191075509605848

while by evaluating the integral numerically we obtain
something different

(C11) B:3\$ A:2\$
romberg(log(1+exp(A+B*cos(phi))),phi,0,%pi);
(C12)
(C13)
(D13) 7.506856487627962
(C14) B:3.2\$ A:-3\$
romberg(log(1+exp(A+B*cos(phi))),phi,0,%pi);
(C15)
(C16)
(D16) 0.663669430006855

The integrand does not look like the kind of thing that
would give the romberg procedure any trouble

(C25) plot2d(log(1+exp(A+B*cos(phi))),[phi,0,%pi])\$

In fact, by visual inspection of the plot it is clear
that the area under the curve is much closer to 0.66
(romberg's result) than to 0.02 (as integrate would
have us believe).

The same problem occurs if we use defint instead of
integrate.

Cheers.

## Discussion

• Robert Dodier
2006-07-31

Logged In: YES
user_id=501686

Observed in 5.9.3cvs. Not sure, but it looks like integrate
yields a different result when A and B are symbols compared
to when they are given specific values A=2, B=3.

• Robert Dodier
2006-07-31

• labels: --> Lisp Core - Integration

• Dan Gildea
2008-11-26

• status: open --> closed

• Dan Gildea
2008-11-26

fixed in risch.lisp rev 1.16 - now returns unevaluated.