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Area enclosed between curves made of sin x and cos x

This type of question, asked 4 times: 2021 Paper 3, 2021 Paper 24, 2021 Paper 26, 29 Jan 2023. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 3

    82
    The graphs of y=sin⁡xy=\sin x and y=cos⁡xy=\cos x intersect at two consecutive points, and between these points the two graphs enclose an area AA. Then A4A^4 is equal to
  2. Question 2

    2021 Paper 24

    71
    The area, enclosed by the curves y=sin⁡x+cos⁡xy= \sin x+ \cos x and y=∣cos⁡x−sin⁡x∣y= |\cos x- \sin x| and the lines x=0,x=π2x= 0,x=\frac{\pi}{2}, is:

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  3. Question 3

    2021 Paper 26

    67
    Let A1A_{1} be the area of the region bounded by the curves y=sin⁡xy = \sin x, y=cos⁡xy = \cos x and yy-axis in the first quadrant. Also, let A2A_{2} be the area of the region bounded by the curves y=sin⁡x,y=cos⁡x,xy = \sin x,y = \cos x,x-axis and x=x = π2\frac{\pi}{2} in the first quadrant. Then,

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  4. Question 4

    29 Jan 2023

    162
    The area of the region A={(x,y):∣cos⁡x−sin⁡x∣≤y≤sin⁡x,0≤x≤π2}A =\left\{ (x,y):|\cos x - \sin x| \leq y \leq \sin x,0 \leq x \leq\frac{\pi}{2} \right\} is

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