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)
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: