Area Between Curves

AP Calculus AB· difficulty 3/5

On [0,2π][0, 2\pi], the total area between y=sinxy = \sin x and y=cosxy = \cos x is

  • A

    222\sqrt 2

  • B

    00

  • C

    22

  • D

    424\sqrt 2

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Explanation

Two intersections in [0,2π][0, 2\pi] at π/4\pi/4 and 5π/45\pi/4. By symmetry, total area is 424\sqrt 2.

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