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Calculus II Quiz
#4 March
11, 2003

Name____________________ R. Hammack Score
______

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(1) Find the area contained between
the graphs of and .

First, let's graph these two functions to see what we are dealing with. The
graph of f is a straight line with
y-intercept 6 and x-intercept
6. Factoring g, we get ,
so you can see that the graph of g
is a parabola that opens "up" and has x-intercepts
0 and 2, and y-intercept 2. Here is
a picture.

So the region we are interested in is the crescent-moon shape contained between
the graph of f (on top) and g
(on the bottom). To find the x
values that bound the region on the left and right, we need to solve to find
the intersection points.

This means the two graphs intersect at the x values of -2 and 3.

Thus the area of the region is

square
units.