Integral Calculus

JEE Main level, single correct, medium

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The area (in sq. units) bounded by the parabola y=x2y = x^2 and the straight line y=2xy = 2x is:

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Answer: (C) 4/34/3

Points of intersection: x2=2x  ⟹  x=0,2x^2 = 2x \implies x=0, 2. Area =∫02(2x−x2) dx=[x2−x3/3]02=4−8/3=4/3= \int_0^2 (2x - x^2)\,dx = [x^2 - x^3/3]_0^2 = 4 - 8/3 = 4/3 sq. units.

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