Area Under the Curve
Area Under Curves
nta_pyq_2025_jan
Grade 12
Question:
Let the area enclosed between the curves |y| = 1 - x and x + y 2 2 2 = 1 be \alpha. If 9\alpha = \beta\pi + \gamma; \beta, \gamma are integers, then the value of |\beta - \gamma| equals.
Step-by-Step Solution
Key Concept: Apply the core result for area bounded by curves and simplify using the given constraints.
(2) 1 2 Required area = \pi - 4\int (1 - x ) dx 0 1 3 x = \pi - 4[x - ] 3 0 2 8 = \pi - 4 \times = \pi - 3 3 8 \therefore \alpha = \pi - 3 9\alpha = 9\pi - 24 \to \beta = 9, \gamma = -24 |\beta - \gamma| = |9 + 24| = 33
Correct Answer: 2