I'm trying to evaluate the surface area of a hemisphere within the
rectangle (-1..1,-1..1). I've managed to get Maxima to give me a
negative number for the surface area, which is quite confusing. When
I do something similar in Maple I get a number near 4.22. What have I
done to confuse Maxima?
Many thanks,
Shaun
z(x,y) := sqrt(4-x^2-y^2);
zx(x,y) := diff( z(x,y), x);
zy(x,y) := diff( z(x,y), y);
N(x,y) := sqrt( 1 + zx(x,y)^2 + zy(x,y)^2);
integrate( integrate( N(x,y), x,-1,1), y,-1,1);
negative
negative
ev(%,limit);
ev(%,integrate);
negative
ev(%,numer);
-8.156085826898927