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Area Between Curves

AP Calculus AB· difficulty 4/5

The area enclosed by y=x2y = x^2 and y=2xy = 2x is

  • A

    83\frac{8}{3}

  • B

    43\frac{4}{3}

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  • C

    13\frac{1}{3}

  • D

    22

Explanation

Intersect: x2=2x⇒x=0,2x^2 = 2x \Rightarrow x=0,2. On [0,2][0,2], line is above parabola. Area =∫02(2x−x2) dx=4−8/3=4/3= \int_0^2(2x-x^2)\,dx = 4 - 8/3 = 4/3.

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