The area between x-axis and curve y = cos x when 0 $\leq$ x $\leq$ 2 $\pi$ is ___________ .

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4 Required shaded area, A = \int_0^$\pi$/2 \cos x dx + \int_$\pi$/2^3$\pi$/2 \left( - \cos x \right)dx + \int_{3$\pi$/2}^{2$\pi$} \cos x dx = \int_0^$\pi$/2 \cos x dx - \int_$\pi$/2^3$\pi$/2 \cos x dx + \int_{3$\pi$/2}^{2$\pi$} \cos x dx = \left[ \sin x \right]_0^$\pi$/2 - \left[ \sin x \right]_$\pi$/2^3$\pi$/2 + \left[ \sin x \right]_{3$\pi$/2}^{2$\pi$} = \left[ \sin x \right]_0^$\pi$/2 - \left[ \sin x \right]_$\pi$/2^3$\pi$/2 + \left[ \sin x \right]_{3$\pi$/2}^{2$\pi$} = \left( 1 - 0 \right) - \left( - 1 - 1 \right) + \left[ 0 - \left( - 1 \right) \right] = 1 + 2 + 1 = 4\text{ sq units } [Solution diagram: 44104_solution_1.png]

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