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Calculus

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Find the area of the region enclosed between y = 2sin (x) and y = 2cos (x) from x = 0 to x = pi/4.

Thanks for your help :)

  • Calculus - ,

    Since cos x > sin x on the interval,

    Integrate 2cos x - 2sin x on [0,pi/4]

    2sin x + 2cos x [0,pi/4]
    at x=pi/4, 2(1/√2 + 1/√2) = 2*2/√2 = 2√2
    at x=0, 2*0 + 2*1 = 2

    area = 2√2 - 2

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