Question
For the following three (03) items: Consider the function f(x) = x|x|. What is the area bounded by the curve f(x), the x-axis and the lines x = -2 and x = 1?
NDA
Mathematics
Area Under Curves
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 1 3
- B. 2 3
- C. 5 2
- D. 3
Answer
D. 3
Step-by-step solution
The given function is f(x) = x|x|. The required area bounded by the curve f(x), the x-axis and the lines x = -2 and x = 1 is given by: A = _ -2 ^ 1 |f(x)| dx A = _ -2 ^ 1 |x|x|| dx Since |x|x|| = |x|^2 = x^2, we have: A = _ -2 ^ 1 x^2 dx A = [ x^3 3 ]_ -2 ^ 1 A = 1^3 3 - (-2)^3 3 A = 1 3 - ( - 8 3 ) A = 9 3 = 3 Answer: 3
Related: Mathematics — Area Under Curves · All PYQ Banks