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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

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To find area under a curve, integrate it. If you integrate cos x with respect to x, you get sin(x) If you directly apply the limits from 0 to 2pi, you will get 0. To find the area, you need to apply limits from 0 to π/2, π/2 to π, 3π/2 and 3π/2 to 2π. Take modulus of each limit and add. You will get the answer as 4. (value of each limit 1)

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I hope you know integration.

You construct small rectangles of height Cos x and width dx along x-axis from x = 0 to x = 2 π. Add the areas of these rectangles to get the answer. Now, from x = 0 to x = π/2, Cos x is positive. Let us take this area and multiply with 4 to get the area from x = 0 to x = 2π.