In an earlier post I described the Maxima package MATH214 for use in my multivariable calculus class. I’ve posted examples with applications to Gauss’s Theorem and Stokes Theorem.

Here we take the double integration routine** integrate2()** and the 2D path integral **integratePathv2()** for a spin with a Green’s Theorem example from Stewart’s Calculus Concepts and Contexts:

And of course polar coordinates are nice too:

The two functions used above are included in the MATH214 package, but I list them below as well.

integratePathv2(H,r,t,a,b):=block( [H2], H2:psubst([x=r[1],y=r[2]],H), integrate( trigsimp(H2.diff(r,t)),t,a,b) ); integrate2(F,xx,aa,bb,yy,cc,dd):=block( integrate(integrate(F,xx,aa,bb),yy,cc,dd));