APPLICATIONS OF THE
6
INTEGRAL
6.1 Area Between Two Curves
Preliminary Questions
1. What is the area interpretation of
Z
b
f .x/
g.x/ dx if f .x/
g.x/?
a
Rb
Because f .x/
g.x/, a .f .x/ g.x/ dx represents the area of the region bounded between the graphs
7
TECHNIQUES OF INTEGRATION
7.1 Integration by Parts
Preliminary Questions
1. Which derivative rule is used to derive the Integration by Parts formula?
SOLUTION
The Integration by Parts formula is derived from the Product Rule.
2. For each of the followin
APPLICATIONS OF
4
THE DERIVATIVE
4.1 Linear Approximation and Applications
Preliminary Questions
1. True or False? The Linear Approximation says that the vertical change in the graph is approximately equal to the vertical
change in the tangent line.
SOLUT
5 THE INTEGRAL
5.1 Approximating and Computing Area
Preliminary Questions
1. What are the right and left endpoints if 2; 5 is divided into six subintervals?
If the interval 2; 5 is divided into six subintervals, the length of each subinterval is
of the su