Multiple integrals

Since MathMate allows nested procedures, it is possible to compute multiple integrals. To compute them, use either Calculator mode or Integration mode. The following example shows how to compute a double integral using the Calculator mode.

Suppose that we need to compute the area of a unit circle. It is represented by a double integral. Enter the following expression:

Int (-1, 1; x, Int (-sqrt(1-x^2), sqrt(1-x^2); y, 1))

and click Start or press Enter.

The result is, as expected, an approximation to p with the number of digits determined by the precision setting. For precision 6 we get

Result: 3.14159
(estimated error 5.8e-8),
 
for precision 9:

Result: 3.14159265
(estimated error 3.2e-10)
 

Precision settings for multiple integrals

It is important to understand that numerical integration is not a precise procedure. Multiple integrals in
MathMate are computed using one-dimensional slices, so the precision requirement is even more restrictive
than for single integrals. Therefore  it is NOT RECOMMENDED to increase precision settings for
multiple integrals as higher precision may be unreachable. In the above example the integrand is a constant,
and still precision above 9 won't work. If the function has oscillations or singularities, it is likely that
computation will fail even for small precisions. The error message that is displayed if the desired precision
is unreachable applies to one of the slice integrals.

See also: