Source: Extra Practice
Find the area bounded by the curve y = |x| and the line y = 1.
Options
Option A
1/2 sq. unit
Option B is correct
1 sq. unit
Option C
2 sq. units
Option D
4 sq. units
Explanation
The region is a triangle with vertices at (0,0), (1,1), and (-1,1). Using integration: Area = ∫[-1 to 1] (1 - |x|) dx = 2 * ∫[0 to 1] (1 - x) dx = 2 * [x - x²/2] from 0 to 1 = 2 * (1 - 1/2) = 1. Geometrically, it is a triangle with base 2 (from x=-1 to 1) and height 1, so Area = 1/2 * 2 * 1 = 1. Options A and C are incorrect factors.