1987 AIME Problems/Problem 4
Problem
Find the area of the region enclosed by the graph of
Solution
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Since is nonnegative,
. Solving this gives us two equations:
. Thus,
. The maximum and minimum y value is when
, which is when
and
. The area of the region enclosed by the graph is that of the quadrilateral defined by the points
. Breaking it up into triangles and solving, we get
.
See also
1987 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |