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Area Between Curves

AP Calculus AB· difficulty 3/5

Area between x=y2x = y^2 and x=y+2x = y + 2, integrated with respect to yy:

  • A

    ∫04(x−(x−2)) dx\int_{0}^{4} (\sqrt x - (x - 2))\,dx

  • B

    ∫−12(y+2−y2) dy\int_{-1}^{2} (y + 2 - y^2)\,dy

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  • C

    Same as A

  • D

    ∫−12(y2−y−2) dy\int_{-1}^{2} (y^2 - y - 2)\,dy

Explanation

yy-strips: right curve is y+2y + 2; left is y2y^2. Bounds where y2=y+2⇒y=−1,2y^2 = y + 2 \Rightarrow y = -1, 2.

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