Hello all :-)
I'm new to sage and to this group.
I teach at a two-year college and have been exploring the
possibilities of incorporating sage into some of my classes. On my
laptop I also have Mathematica and Matlab installed and have used
Maple in the past as well.
I started experimenting with sage because it would provide a free
(yay!) alternative to the programs mentioned above; this is a big plus
for my students already burdened with the high cost of their
textbooks. With the small amount of exposure to sage I've had so far,
I can say that I find it useful and powerful. It is also, to me,
confusing at time but to be fair so too are Mathematica and Maple.
Now to the problem at hand.
I've been trying to evaluate a symbolic double integral but am
perplexed by the unevaluated tan(pi/2) expressions in the result since
tan(pi/2) is undefined. What am I missing here and what do I need to
do to get this to evaluate to the correct value of
(4*pi - 3*sqrt(3))*a^2/6?
Thanks much,
Gary
sage input:
***************************************************************
var('a r theta')
assume(a > 0)
integral(integral(r, r, a*csc(theta), 2*a), theta, pi/6, pi/2)
***************************************************************
sage output:
*********************************************************************
(2*pi*tan(pi/2) + 1)*a^2/(2*tan(pi/2)) - (2*pi + 3*sqrt(3))*a^2/6
*********************************************************************
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