_________________________________________________________________________________
Calculus II Quiz
#4 March
11, 2003
Name____________________ R. Hammack Score
______
_________________________________________________________________________________
(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.