The area of the region bounded by the curve y | vedclass

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(C) The area bounded by the curve $y = \cos x$ from $x = 0$ to $x = \pi$ is given by the integral of the absolute value of the function: $	ext{Area}

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$2$ sq. unit

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(C) The area bounded by the curve $y = \cos x$ from $x = 0$ to $x = \pi$ is given by the integral of the absolute value of the function: $	ext{Area} = \int_{0}^{\pi} |\cos x| \, dx$ Since $\cos x \ge 0$ for $x \in [0, \pi/2]$ and $\cos x \le 0$ for $x \in [\pi/2, \pi]$,we split the integral: $	ext{Area} = \int_{0}^{\pi/2} \cos x \, dx + \int_{\pi/2}^{\pi} (-\cos x) \, dx$ Evaluating the integrals: $= [\sin x]_{0}^{\pi/2} + [-\sin x]_{\pi/2}^{\pi}$ $= (\sin(\pi/2) - \sin(0)) + (-(\sin(\pi) - \sin(\pi/2)))$ $= (1 - 0) + (-(0 - 1))$ $= 1 + 1 = 2 	ext{ sq. units.}$

The area of the region bounded by the curve $y = \cos x$ between $x = 0$ and $x = \pi$ is

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