Area Between Two Curves

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# Area Between Two Curves - PowerPoint PPT Presentation

Area Between Two Curves. 7.1. 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…. .

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### Area Between Two Curves

7.1

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
Example 4
• Find the area of the region that is enclosed between the curves x = y² and y = x – 2
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

#2

• 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)