Function: PVInt - numerical principal value integral
PVint(f, x=a..b, p)
f - the integrand, expression in one variable x
x - name
a, b - real constants, the endpoints of the integration
p - real constant, location of a singularity in the interval of integration
> PVInt(tan(x), x = 0 .. 2, Pi/2);
This one could have been integrated symbolically.
The singularity at would cause ordinary numerical integration to fail.
Error, (in evalf/int) numeric exception: invalid operation
The next one can not be integrated symbolically: presumably there is no closed form for the integral.
The next one diverges.
> PVInt(1/(sin(x)^3+x^4), x=-1..2, 0);
The location of the singularity must be known exactly. A floating-point approximation would not be enough.
> p0:= fsolve(exp(x)-3*x,x=0..1);
Error, (in evalf/int) unable to handle singularity
Since it depends on finding a finite number of terms with negative exponents in the Laurent series, PVInt will not work with singularities that are essential or non-isolated. For example, the following principal value integral is 0 by symmetry, but PVInt can't evaluate it.
Error, (in numapprox[laurent]) unable to compute Laurent series
int , int[numeric]
Maple Advisor Database R. Israel, 2000