Area Under the Curve
Area Under Curves
nta_pyq_2025_jan
Grade 12
Question:
The area of the region, inside the circle (x - 2\sqrt3) + y2 2 = 12 and outside the parabola y 2 = 2\sqrt3x is :
3\pi + 8
6\pi - 16
3\pi - 8
6\pi - 8
Step-by-Step Solution
Key Concept: Apply the core result for area bounded by curves and simplify using the given constraints.
(2) 2\sqrt3 2 Required area = 2\int (\sqrt4\sqrt3x - x - \sqrt2\sqrt3x) dx 0 2\sqrt3 2 = 2\int (\sqrt12 - (x - 2\sqrt3) - \sqrt2\sqrt3x) dx 0 x - 2\sqrt 3 12 x - 2\sqrt 3 2 -1 = 2[ \sqrt12 - (x - 2\sqrt3) + sin ( ) 2 2 2\sqrt 3 3 2\sqrt3 \sqrt2\sqrt3x 2 ⎤ - 3 ⎦ 2 0 = 2{3\pi - 8} = 6\pi - 16 sq. units.
Correct Answer: 2