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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.