Question
Passage: Consider the curves y=x^2 and y=2|x|. Question: What is the area bounded by the curves, the lines x=0 and x=1 ?
NDA
Mathematics
Area Under Curves
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. 1 square unit
- B. 2 3 square unit
- C. 1 2 square unit
- D. 1 3 square unit
Answer
B. 2 3 square unit
Step-by-step solution
For x [0, 1], the curve y = 2|x| becomes y = 2x. In the interval x [0, 1], 2x x^2. The required area is given by the integral: A = _ 0 ^ 1 (2x - x^2) dx A = [ x^2 - x^3 3 ]_ 0 ^ 1 A = 1 - 1 3 = 2 3 square units.
Related: Mathematics — Area Under Curves · All PYQ Banks