Lesson 6-1b

1
Lesson 6-1b

• Area Between Curves

2
Ice Breaker

• Homework Check
• (Setup only) Find the area between y 9 x²,
  y ½ x and the lines x-1 and x 2
• Reading questions none

3
Objectives

• Find the area between two curves
• Using either x (vertical rectangles) or
• y (horizontal rectangles) as the variable of
  integration

4
Vocabulary

• Area under curve definite integral of the curve
  evaluated between two endpoints
• Area between curves definite integral of the
  height (usually the difference in the curves)
  evaluated between two point (can be points of
  intersection or just two arbitrary points)

5
Area under the Curve
6
Example 4
7
Example 5
8
Example 6
Step 1 Find intersection points Step 2 Rough
Graph Step 3 Determine
vertical (top bottom) dx or
horizontal (right left) dy Step 4 Solve
9
In General
top curve bottom curve
right curve left curve
j(y)
g(x)
d
dx
f(x)
h(y) j(y)
f(x) g(x)
dy
h(y)
c
b
a
10
Example 7
right curve left curve
top curve bottom curve
f(x) ?x
dx
h(y) j(y)
g(x) x²
1
dy
f(x) g(x)
1
11
Summary Homework

• Summary
• Area between curves is still a height times a
  width
• Width is always dx (vertical) or dy (horizontal)
• Height is the difference between the curves or
  between a curve and a line
• Homework
• pg 442 - 442 2, 12, 15, 17