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Area Between Curves

AP Calculus AB· difficulty 2/5

Find the area between y=xy = x and y=x2y = x^2 on [0,1][0, 1].

  • A

    11

  • B

    13\tfrac{1}{3}

  • C

    12\tfrac{1}{2}

  • D

    16\tfrac{1}{6}

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Explanation

∫01(x−x2) dx=[x2/2−x3/3]01=1/2−1/3=1/6\int_0^1 (x - x^2)\,dx = [x^2/2 - x^3/3]_0^1 = 1/2 - 1/3 = 1/6.

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