Area Under the Curve
Area — passage based
Grade 12
Question:
<p>Area of region bounded by \(y=x\) and \(y=x^3\) for \(x\in[0,1]\). [JEE Advanced 2012]</p>
Step-by-Step Solution
Key Concept: On [0,1]: x \geq x^3. Area = \int_0^1(x-x^3)dx = 1/2-1/4 = 1/4.
<div class='solution'>
<p>$$A=\int_0^1(x-x^3)dx=\left[\frac{x^2}{2}-\frac{x^4}{4}\right]_0^1=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$$</p>
</div>
Correct Answer: A