Definite Integration
Piecewise Functions
JEE Main 2020
Grade 12
Question:
$\int_0^2 |1 - x| \, dx$ equals:
(1) $1$
(2) $2$
(3) $\frac{1}{2}$
(4) $\frac{3}{2}$
Step-by-Step Solution
Key Concept: Split the interval at $x = 1$ — where the expression inside the modulus changes sign — and integrate $(1 - x)$ on one piece and $(x - 1)$ on the other.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)