Area Under the Curve
Area Under Curves
nta_pyq_2025_jan
Grade 12
Question:
If the area of the larger portion bounded between the curves x + y 2 2 = 25 and y = |x - 1| is 1 4 (b\pi + c), b, c \in N , then b + c is equal to
Step-by-Step Solution
Key Concept: Apply the core result for area bounded by curves and simplify using the given constraints.
(77) 2 2 x + y = 5 2 2 x + (x - 1) = 25 \Rightarrow x = 4 2 2 x + (-x + 1) = 5 \Rightarrow x = -3 4 1 1 2 A = 25\pi - \int \sqrt25 - x dx + \times 4 \times 4 + \times 3 \times 3 2 2 -3 4 25 x 25 x 2 -1 A = 25\pi + - [ \sqrt25 - x + sin ] 2 2 2 5 -3 25 25 4 25 3 -1 -1 A = 25\pi + - [6 + sin + 6 + sin ] 2 2 5 2 5 1 25 \pi A = 25\pi + - ⋅ 2 2 2 75\pi 1 A = + 4 2 1 A = (75\pi + 2) 4 b = 75, c = 2 b + c = 75 + 2 = 77
Correct Answer: 77