<p>Area bounded by \(y=x-x^2\) and the \(x\)-axis. [JEE Main 2019]</p>
Step-by-Step Solution
Key Concept: Roots at x=0,1. Area = \int_0^1(x-x^2)dx = 1/2-1/3 = 1/6.
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<p>$y=x-x^2=x(1-x)$. Roots: $x=0,1$.</p>
<p>$$A=\int_0^1(x-x^2)dx=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$$</p>
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Correct Answer: B