(a)
(b)
(c)
(a)
(b)
(c)
Example 33 is an excellent instance of the FTC: if f = F ′, then gives the
total change in F as x varies from a to b.
Example 34 __
Suppose . Evaluate
SOLUTIONS:
9.To evaluate , let u = x − 3. Then du = dx and, when x = 2, u = −1;
when x = 7, u = 4. Therefore .G. INTERPRETING ln X AS AN AREA
It is quite common to define ln x, the natural logarithm of x, as a definite
integral, as follows:
.This integral can be interpreted as the area bounded above by the curve
, below by the t-axis, at the left by t = 1, and at the right by t = x (x > 1). See
Figure N6–16.