Area Under the Curve
Area Under a Curve
JEE Main 2018
Grade 12
Question:
The area bounded by the curve $y = x^3$, the $x$-axis, and the ordinates $x = -1$ and $x = 1$ is:
(1) $\frac{1}{2}$
(2) $0$
(3) $\frac{1}{4}$
(4) $1$
Step-by-Step Solution
Key Concept: Use symmetry: $|x^3|$ is an even function, so the required (geometric) area is twice the area between $x = 0$ and $x = 1$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)