Area of a Region Between Two Curves (7.1)

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Area of a Region Between Two Curves (7.1) April 12th, 2012

I. Area of a Region Between Two Curves Area of a Region Between Two Curves: If f and g are continuous on [a, b] and for all x in [a, b], then the area of the region bounded by the graphs of f and g and the vertical lines x=a and x=b is .

Ex 1: Find the area of the region bounded by the graphs of , , , and .

You Try: Find the area of the region bounded by the graphs of , , , and .

II. Area of a Region Between Two Intersecting Curves *Calculate the upper and lower limits of the integral by determining where the two graphs intersect.

Ex. 2: Find the area of the region bounded by the graphs of and .

You Try: Find the area of the region bounded by the graphs of and .

*If a set of two curves intersects at more than two points, use multiple integrals to evaluate the area.

Ex. 3: Find the area of the region bounded by the graphs of and .

You Try: Find the area of the region bounded by the graphs of and .

*It is sometimes useful to integrate with respect to y, which means using horizontal rectangles in setting up the integral.

Ex. 4: Find the area of the region bounded by the graphs of f(y)=y(2-y) and g(y)=-y.

You Try: Find the area of the region bounded by the graphs of , g(y)=0, and y=3.