Area Under the Curve
Area Under Curves
nta_pyq_2025_jan
Grade 12
Question:
Let the area of the region {(x, y) : 2y \le x 2 + 3, y + ∣x∣ \le 3, y \ge ∣x - 1∣} be A. Then 6 A is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for area bounded by curves and simplify using the given constraints.
(3) A \Rightarrow Rectangle ABDE - Area of region EDC 1 2 x + 3 A \Rightarrow 4 - 2\int (3 - x) - ( ) dx 2 0 1 2 3 x x 3 A \Rightarrow 4 - 2{3x - - - x} 2 6 2 0 1 1 3 7 A \Rightarrow 4 - 2 {3 - - - } = 2 6 2 3 So 6 A = 14
Correct Answer: 3