Area Under the Curve
Area Under Curves
nta_pyq_2025_jan
Grade 12
Question:
The area of the region enclosed by the curves y = e , y = |e - 1| and y-axis is: x x
1 - log 2 e
log 2 e
1 + log 2 e
2 log 2 - 1 e
Step-by-Step Solution
Key Concept: Apply the core result for area bounded by curves and simplify using the given constraints.
(1) x x x e = 1 - e \Rightarrow 2e = 1 1 x \Rightarrow e = 2 1 \Rightarrow x = ln 2 0 x x \int [e - (1 - e )] dx ln(1/2) 0 x x 0 = \int (2e - 1) dx = 2e - x| - ln 2 ln 2 = 2 - (1 + ln 2) = 1 - log 2 e
Correct Answer: 1