∫_(−(π/2)) ^(π/2) {sin∣x∣+cos∣x∣} dx


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Question Number 67572 by aliesam last updated on 28/Aug/19
$∫_(−(π/2)) ^(π/2) {sin∣x∣+cos∣x∣} dx$
$\int_{- \frac{π}{2}}^{\frac{π}{2}} {s i n ∣ x ∣ + c o s ∣ x ∣} d x$
Commented by mathmax by abdo last updated on 28/Aug/19
$∫_(−(π/2)) ^(π/2) (sin∣x∣ +cos∣x∣)dx =2 ∫_0 ^(π/2) {sinx +cosx} dx =2[−cosx +sinx]_0 ^(π/2) =2{1−(−1)} =4$
$\int_{- \frac{π}{2}}^{\frac{π}{2}} (s i n ∣ x ∣ + c o s ∣ x ∣) d x = 2 \int_{0}^{\frac{π}{2}} {s i n x + c o s x} d x$ $= 2 {[- c o s x + s i n x]}_{0}^{\frac{π}{2}} = 2 {1 - (- 1)} = 4$
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