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6.1 part 2 Area Between two Curves Blank.notebook
1
March 31, 2017
Area between Relations/Functions using Horizontal Rectangles
Due to the properties of functions (Vertical Line Test), Vertical rectangles can be used the majority of the time to find area between two functions. With relations however, it is often easier to use "horizontal rectangles" to determine area between two curves the formula can be amended in following manner.
Vertical Rectangles
Horizontal Rectangles
6.1 Area Between Two Curves Part 2
Example 1: Find the area of the region bounded by the curves and .
4 3 2 1 0 1 2 3 4
4
3
2
1
1
2
3
4
x
yMethod 1: Vertical Rectangles
6.1 part 2 Area Between two Curves Blank.notebook
2
March 31, 2017
Example 2: Find the area of the region bounded by the curves and .
4 3 2 1 0 1 2 3 4
4
3
2
1
1
2
3
4
x
yMethod 2: Horizontal Rectangles
Example 3: Determine area of the figure with vertices (2,4), (3,1), (6,1) and (3,4) using integration.
6 5 4 3 2 1 0 1 2 3 4 5 6
6
5
4
3
2
1
1
2
3
4
5
6
x
y
Example 4: Verify your results from Example 4 Geometrically
6.1 part 2 Area Between two Curves Blank.notebook
3
March 31, 2017