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CUET · MATHS · PYQ PAPER 2023

The area enclosed between the curves \(y=x^2\) and \(x=y^2\) is

  1. A 1
  2. B \(\frac{1}{2}\)
  3. C \(\frac{1}{3}\)
  4. D \(\frac{1}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{3}\)

Step-by-step Solution

Detailed explanation

\(x=y^2 \implies y=\sqrt{x}\) Intersections: \(x^2=\sqrt{x} \implies x^4=x \implies x(x^3-1)=0 \implies x=0, x=1\) Area \(=\int_0^1 (\sqrt{x}-x^2) dx\) \(=\left[\frac{2}{3}x^{3/2}-\frac{1}{3}x^3\right]_0^1\) \(=\frac{2}{3}(1)^{3/2}-\frac{1}{3}(1)^3 - (0-0)\)…