WBJEE · Maths · Area Under Curves
The area enclosed between \(y^2=x\) and \(y=x\) is
- A \(\frac{2}{3}\) sq. units
- B \(\frac{1}{2}\) units
- C \(\frac{1}{3}\) units
- D \(\frac{1}{6}\) units
Answer & Solution
Correct Answer
(D) \(\frac{1}{6}\) units
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Hints: } A=\int_0^1(\sqrt{x}-x) d x \\ & =\frac{2}{3}\left(x^{3 / 2}\right)_0^1-\frac{1}{2}\left(x^2\right)_0^1=\frac{2}{3}[1-0]-\frac{1}{2}[1-0] \\ & =\frac{2}{3}-\frac{1}{2}=\frac{4-3}{6}=\frac{1}{6}\end{aligned}\)
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