Area Under the Curve
Area Under a Curve
IIT-JEE 1999
Grade 12
Question:
The area bounded by the curve $y = x|x|$, the $x$-axis, and the ordinates $x = -1$ and $x = 1$ is:
(1) $\frac{2}{3}$
(2) $\frac{1}{3}$
(3) $\frac{4}{3}$
(4) $0$
Step-by-Step Solution
Key Concept: Note that $y = x|x|$ behaves differently for $x < 0$ and $x > 0$ — split the region at $x = 0$ and integrate $|y|$ on each piece separately.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)