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Area Between Two CurvesPowerPoint Presentation

Area Between Two Curves

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Area Between Two Curves

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Area Formula

- If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the area of the region bounded above by y = f(x), below by y = g(x), on the left by x = a and on the right by x = b is….

Example 1

- Find the area of the region bounded above by y = x + 6 and below by y = x², and bounded on the sides by the lines x = 0 and x = 2.

Example 1

- Find the area of the region bounded above by y = x + 6 and below by y = x², and bounded on the sides by the lines x = 0 and x = 2.

Example 2

- Find the area of the region that is enclosed between the curves y = x² and y = x + 6

Example 2

- Find the area of the region that is enclosed between the curves y = x² and y = x + 6

Example 3

- Find the area enclosed by the curves
and

Example 3

- Find the area enclosed by the curves
and

Practice

- Sketch the region enclosed by and then find the area.

Practice

- Sketch the region enclosed by and then find the area.

Example 4

- Find the area of the region that is enclosed between the curves x = y² and y = x – 2
- What’s different about this question?

Example 4

- Find the area of the region that is enclosed between the curves x = y² and y = x – 2
- What’s different about this question?

Two ways to solve…..

#1

- Subdivide the regions
- Equation of top graph – equation of bottom graph
- Equations must be solved in terms of y and bound are determined by x values

- Reverse the roles of x and y
- When reversing roles you always subtract the graph on the right – graph on left
- Must solve equations in terms of x and gets bounds in terms of y

Example 5

- Find the area of the region enclosed by the curves and x = 1.

Example 6

- Find the area of the region enclosed by the curves and

Practice

- Pg. 448 (1 – 23 odd)