5.2
The Definite Integral
3 2 1 0 -1 2 0 -2 -4 x y x ySuppose () is a function that is continuous on an interval and and are numbers in the interval such that If we have a formula for () we can find the change () as increasing from to by simply computing
()− ()
Theorem 60 Let () be a function that is continuous on an interval, and and be numbers in the interval such that Suppose () is a function whose derivative is () If () is any antiderivative of () the amount () changes if increasing from to is
()− ()
Definition 26 Let () be a function that is continuous on an interval, and let and be numbers in the interval such that . Suppose () is an antiderivative of () The definite integral of () from = to = is the number obtaine / by
Z () = ()|== = ()− () Example 124 Compute Z 15 3 7 Example 125 Compute Z 10 4 −8 2 66
Example 126 Compute Z 12 9 µ 1 15 2 − 2 + 20 ¶ 67
