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Question Number 95227 by bobhans last updated on 24/May/20

$$\underset{-\pi }{\stackrel{\pi }{\int }}\mid \sin \mathrm{x}+\cos \mathrm{x}\mid \mathrm{dx}=?$$

Answered by john santu last updated on 24/May/20

Commented by john santu last updated on 24/May/20

$$\underset{-\pi }{\stackrel{-\frac{\pi }{4}}{\int }}(\sin \mathrm{x}+\cos \mathrm{x})\mathrm{dx}+\underset{-\frac{\pi }{4}}{\stackrel{\frac{3\pi }{4}}{\int }}(\sin \mathrm{x}+\cos \mathrm{x})\mathrm{dx}+\underset{\frac{3\pi }{4}}{\stackrel{\pi }{\int }}(\sin \mathrm{x}+\cos \mathrm{x})\mathrm{dx}=$$$$2\underset{-\frac{\pi }{4}}{\stackrel{\frac{3\pi }{4}}{\int }}(\sin \mathrm{x}+\cos \mathrm{x})\mathrm{dx}=$$$$2{[-\cos \mathrm{x}+\sin \mathrm{x}]}_{-\frac{\pi }{4}}^{\frac{3\pi }{4}}=$$$$2\{\sqrt{2}-(-\sqrt{2})\}=4\sqrt{2}$$

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