Double Integrals

We can iterate integrate calls. For example, suppose we wanted to calculate

$\begin{displaymath} \int\int \left(x^3 - 3xy\right) \mathrm{d}y \mathrm{d}x. \end{displaymath}$

$\begin{maximasession} f(x,y) := x^3 - 3*x*y; integrate(integrate(f(x,y), y), x);... ... x); \\ \o2. {{x^4 y}\over{4}}-{{3 x^2 y^2}\over{4}} \\ \end{maximasession}$

Maxima does not provide arbitrary constants of integration; the user must remember them. It is easy to do definite integration, for example, we could do

$\begin{displaymath} \int_0^1\int_{\sqrt{x}}^{2-x} \left(x^3 - 3xy\right) \mathrm{d}y \mathrm{d}x. \end{displaymath}$

with
$\begin{maximasession} integrate(integrate(f(x,y), y, x^1/2, 2 - x), x, 0, 1); \m... ... y, x^1/2, 2 - x), x, 0, 1); \\ \o3. -{{173}\over{160}} \\ \end{maximasession}$

G. Jay Kerns 2009-12-01