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Question Number 85846 by Jakir Sarif Mondal last updated on 25/Mar/20

$$\underset{0}{\stackrel{50\pi }{\int }}\mid \cos x\mid dx=$$

Commented by jagoll last updated on 25/Mar/20

$$100\times \int \underset{0}{\stackrel{\frac{\pi }{2}}{}}\cos \mathrm{x}\mathrm{dx}$$$$=100\times \left[\sin \mathrm{x}\right]{\underset{0}{}}^{\frac{\pi }{2}}$$$$=100$$

Commented by mathmax by abdo last updated on 25/Mar/20

$$I=\sum _{k=0}^{49}{\int }_{k\pi }^{(k+1)\pi }\mid cosx\mid dx{=}_{x=k\pi +u}\sum _{k=0}^{49}{\int }_0^{\pi }\mid cos(k\pi +u)\mid du$$$$=\sum _{k=0}^{49}{\int }_0^{\pi }\mid cosu\mid du=\sum _{k=0}^{49}({\int }_0^{\frac{\pi }{2}}cosudu-{\int }_{\frac{\pi }{2}}^{\pi }cosudu)$$$$50{\left[sinu\right]}_0^{\frac{\pi }{2}}-50{\left[sinu\right]}_{\frac{\pi }{2}}^{\pi }=50-50(-1)=50+50=100$$$$\Rightarrow I=100$$

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