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The area enclosed between the curves y=x2y = x^2 and x=y2x = y^2 is

Solution

✅ Correct Option: 3

Curves y=x2y = x^2 and x=y2x = y^2 (i.e. y=xy = \sqrt{x}) intersect at (0,0)(0, 0) and (1,1)(1, 1). Area =∫01(x−x2) dx=[2x3/2/3−x3/3]01=2/3−1/3=1/3= \int_0^1 (\sqrt{x} - x^2)\,dx = [2x^{3/2}/3 - x^3/3]_0^1 = 2/3 - 1/3 = 1/3.

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