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Area Between Curves

AP Calculus AB· difficulty 3/5

x y=x² y=x

The area between y=xy = x and y=x2y = x^2 on [0,1][0,1] equals:

  • A

    16\tfrac{1}{6}

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  • B

    13\tfrac{1}{3}

  • C

    11

  • D

    12\tfrac{1}{2}

Explanation

∫01(x−x2) dx=12−13=16\int_0^1 (x - x^2)\,dx = \tfrac12 - \tfrac13 = \tfrac{1}{6}.

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