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Question Number 67572 by aliesam last updated on 28/Aug/19

∫_(−(π/2)) ^(π/2) {sin∣x∣+cos∣x∣} dx

$$\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \left\{{sin}\mid{x}\mid+{cos}\mid{x}\mid\right\}\:{dx} \\ $$

Commented by mathmax by abdo last updated on 28/Aug/19

∫_(−(π/2)) ^(π/2)  (sin∣x∣ +cos∣x∣)dx =2 ∫_0 ^(π/2) {sinx +cosx} dx  =2[−cosx +sinx]_0 ^(π/2)  =2{1−(−1)} =4

$$\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \:\left({sin}\mid{x}\mid\:+{cos}\mid{x}\mid\right){dx}\:=\mathrm{2}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left\{{sinx}\:+{cosx}\right\}\:{dx} \\ $$$$=\mathrm{2}\left[−{cosx}\:+{sinx}\right]_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:=\mathrm{2}\left\{\mathrm{1}−\left(−\mathrm{1}\right)\right\}\:=\mathrm{4} \\ $$

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