1987 AIME Problems/Problem 4
Problem
Find the area of the region enclosed by the graph of
Solution
Since is nonnegative, . Solving this gives us two equations: . Thus, . The maximum and minimum y value is when , which is when and . Since the graph is symmetric about the y-axis, we just need casework upon . , so we break up the condition :
- . Then .
- . Then .
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 | ||
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