The definite integral
f (x)dx of a
function f (x) defined on the interval [a, b] is
given by
If f is integrable on [a, b], then
Definite integrals can be evaluated in the same way as indefinite integrals: Leave the insertion point in the expression and choose Evaluate or Evaluate Numerically.
To enter a definite integral
Evaluate, Evaluate Numerically
x2
dx =
-
= .4063171388
Evaluate Numerically
x2
dx = .4063171388
The following examples are easily handled by Scientific Notebook. Choose Evaluate or Evaluate Numerically to compute these integrals.
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Integrals involving absolute values or piecewise-defined functions can now be treated like any other function.
Note: You should use special care when working with improper integrals. Make sure answers look reasonable. Neither machines nor people are infallible, but people and machines working together can accomplish more than either can working alone or unattended.
Note This improper integral is examined further in the exercises at the end of this chapter.