The area of the region bounded by the curves x (1 + y ) = 1 and y 2 2 = 2x is:
Step-by-Step Solution
Key Concept: Apply the core result for area bounded by curves and simplify using the given constraints.
2 x (1 + y ) = 1 (2) 2 y = 2x From equation (1) \& (2) 2 x(1 + 2x) = 1 \Rightarrow 2x + x - 1 = 0 1 \Rightarrow x = , x = -1 (Reject) 2 1 2 \Rightarrow y = 2( ) 2 \Rightarrow y = $\pm$1 1 2 1 y Area bounded = \int ( - ) dy -1 1 + y 2 2 1 ∣ 3 y -1 ∣ = (tan y - ) ∣ 6 ∣ -1 \pi 1 = - 2 3
Correct Answer: 2