int_0^pi |cos x| , dx = | vedclass

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(C) We need to evaluate the integral $I = \int_0^\pi |\cos x| \, dx$. Since $\cos x \ge 0$ for $x \in [0, \pi/2]$ and $\cos x \le 0$ for $x \in [\pi/2

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$2$

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(C) We need to evaluate the integral $I = \int_0^\pi |\cos x| \, dx$. 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: $I = \int_0^{\pi/2} \cos x \, dx + \int_{\pi/2}^\pi (-\cos x) \, dx$. Evaluating the first part: $\int_0^{\pi/2} \cos x \, dx = [\sin x]_0^{\pi/2} = \sin(\pi/2) - \sin(0) = 1 - 0 = 1$. Evaluating the second part: $\int_{\pi/2}^\pi -\cos x \, dx = -[\sin x]_{\pi/2}^\pi = -(\sin(\pi) - \sin(\pi/2)) = -(0 - 1) = 1$. Adding both parts: $I = 1 + 1 = 2$.

$\int_0^\pi |\cos x| \, dx = $

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