Integration

[henningsogaard]

Why don't Mathcad 15 and Mathcad Prime 2.0 come up with an answer when ask for the integral of b*sqrt(1-(x/a)^2) from x = 0 to x = a? My TI-89 calculater and Maple come up with the answer right away (pi*a*b/4, i.e. the area of an ellipse with axes a and b). Regards, Henning

[RichardJ]

In general, the Mupad symbolic engine is not very good with integrals, especially definite integrals. In this case it's a question of assumptions though. That solution is only valid for a>0, and when I try it using the Maple engine in earlier versions of Mathcad Maple does not claim otherwise. It seems Mupad gets it wrong for a<0 though.

[henningsogaard]

Thank you for your very useful answer. Did you use Maple 16 in your examples? With Maple 16 I get a*b*pi/4 whether or not I assume positive or negative a. This corresponds with the fact that if you accept signed area this answer is generally valid.

[RichardJ]

Mathcad 14, 15 and Prime use MuPad as the symbolic engine. Mathcad 13 and earlier use Maple as the symbolic engine, but an older version of Maple (the copyright is 1994). That's what I used. I don't have a copy of Maple itself.