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4.2 Area Greenfield Village, Michigan
Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002
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Objectives Understand the concept of area.
Approximate the area of a plane region. Find the area of a plane region using limits.
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Calculator Lab: DrawRec
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Theorem 4.3: Limit of the Lower and Upper Sums
(If n∞, upper sum = lower sum)
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Definition of the Area of a Region in the Plane: Let f be a continuous and nonnegative function on [a,b]. The area of the region bounded by the graph of f, the x-axis, and the vertical lines x=a and x=b is Steps:
![Definition of the Area of a Region in the Plane: Let f be a continuous and nonnegative function on [a,b]. The area of the region bounded by the graph of f, the x-axis, and the vertical lines x=a and x=b is](http://slideplayer.com./slide/16533900/96/images/6/Definition+of+the+Area+of+a+Region+in+the+Plane%3A+Let+f+be+a+continuous+and+nonnegative+function+on+%5Ba%2Cb%5D.+The+area+of+the+region+bounded+by+the+graph+of+f%2C+the+x-axis%2C+and+the+vertical+lines+x%3Da+and+x%3Db+is.jpg "Steps:")
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Example: Find the area of the region bounded by the graph of f(x)=x3, the x-axis and the vertical lines x=0 and x=1.
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Example: Find the area of the region bounded by the graph of f(x)=4-x2, the x-axis and the vertical lines x=1 and x=2.
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Example: Find the area of the region bounded by the graph of f(y)=y2, the y-axis and 0≤y≤1.
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Homework 4.2 (page 262) #47-51 odd #63
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