| | | Integration bugs |
All computer programs have bugs, politely known as "features". Maple has its share. Although the developers continually correct programming errors, they also continue to introduce new ones.
Sometimes Maple gets symbolic antiderivatives wrong. Dave Rusin posted the following example to the newsgroup sci.math.symbolic on March 10, 1999, with the wry comment, "I had always wanted my calculus students to have the same skills as Maple; unfortunately I seem to have gotten my wish."
> f:=x->x^(-1)*sqrt(ln(x))/sqrt(x-1);
sqrt(ln(x))
f := x -> -------------
x sqrt(x - 1)
> int(f(x),x);
(3/2)
ln(x)
2 -----------
sqrt(x - 1)
> f(x)-diff(int(f(x),x),x);
(3/2)
sqrt(ln(x)) ln(x)
-2 ------------- + ------------
x sqrt(x - 1) (3/2)
(x - 1)
Maple has got the antiderivative wrong: indeed, the derivative of Maple's antiderivative is not equal to the original function.
On 3 September 2001, Preben Alsholm posted the following bug, new in Maple 7, to the newsgroup comp.soft-sys.math.maple:
> evalf(int(x/surd(x^2-9,5), x=-4..5));
evalf(Int(x/surd(x^2-9,5), x=-4..5));
-8
-.6893681372 10
2.778944029
The two answers ought to be the same.
The Math 696 course
pages were last modified April 5, 2005. | | | Integration bugs |