Area Under the Curve
Area Under Curves
nta_pyq_2025_jan
Grade 12
Question:
The area of the region {(x, y) : x + 4x + 2 \le y \le |x + 2|} is equal to 2
Step-by-Step Solution
Key Concept: Apply the core result for area bounded by curves and simplify using the given constraints.
x 2 + 4x + 2 \le y \le |x + 2| (4) 0 1 2 A1 = \int [2 - (x + 4x + 2)] dx - \times 4 \times 2 2 -4 0 3 -x 2 = ( - 2x ) - 4 3 -4 64 = 0 - ( - 32) - 4 3 64 20 = 32 - - 4 = 3 3
Correct Answer: 4