| ||||||||||||||||||
Definite Integrals
integrate(expression, start, end) integrates the expression (as a function of the
variable x) over the range x = start to x = end.
For example: integrate(x*x, 3, 6) returns 63.
Another example: 2*integrate(exp(-x*x/2), 0, sd)/sqrt(2*pi) calculates the probability that
a normally distributed variable falls within sd standard deviations of the mean.
Accuracy
The greater the accuracy desired for an integration, the longer it will take to compute. As the optimum accuracy is always a compromise, UltimaCalc allows you to decide. To do this, use the menu item Options / Other and choose the Numbers tab.
Certain expressions may be very difficult to integrate, and if UltimaCalc fails to achieve a reasonable level of accuracy, it will inform you. A more likely problem is that of encountering a singularity.
Example:
integrate(tan(x), 0, pi)
UltimaCalc will inform you that there is probably a singularity at 1.570796. This is indeed the case.
The value of the variable x is not changed; if it did not
exist before integrate was executed, it will not exist
afterwards, either. Some complex expressions, especially user-defined
functions, can take a few moments to integrate.