Question
Consider the following for the two (02) items that follow: Let the function f(x) = x^2 - 1. What is the area bounded by the function f(x) and the x-axis?
NDA
Mathematics
Area Under Curves
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 1 3 square unit
- B. 2 3 square unit
- C. 4 3 square units
- D. 2 square units
Answer
C. 4 3 square units
Step-by-step solution
The curve intersects the x-axis when f(x) = 0. x^2 - 1 = 0 x = -1, 1 The required area is given by A = _ -1 ^ 1 |x^2 - 1| dx. Since x^2 - 1 0 for x [-1, 1], we have: A = _ -1 ^ 1 (1 - x^2) dx A = [ x - x^3 3 ]_ -1 ^ 1 A = ( 1 - 1 3 ) - ( -1 + 1 3 ) A = 2 3 - ( - 2 3 ) = 4 3 square units. Answer: 4 3 square units
Related: Mathematics — Area Under Curves · All PYQ Banks