Is maxima consistent with the fundamental theorem of calculus? Consider the following:
depends(x,t)$
integrate(diff(x,t),t);
just gives me
/
[ dx
(%o2) I -- dt
] dt
/
which I can't really use. I'd like it to give me x+C where C doesn't depend on time t. And in case I specify the limits (say t0,t1) for the integral, I should get x(t1)-x(t0).
Does anyone know if maxima supports this behavior?
According to the documentation:
integrate works only with functional relations represented explicitly with the f(x) notation. integrate does not respect implicit dependencies established by the depends function.
For example, with an explicit function:
(%i1) integrate(diff(x(t), t), t);
(%o1) x(t)