pi-pi-sin-x-cos-x-dx-

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

\underset{- π}{\int^{π}} ∣ \sin x + \cos x ∣ dx = ?

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

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

\underset{- π}{\int^{- \frac{π}{4}}} (\sin x + \cos x) dx + \underset{- \frac{π}{4}}{\int^{\frac{3 π}{4}}} (\sin x + \cos x) dx + \underset{\frac{3 π}{4}}{\int^{π}} (\sin x + \cos x) dx =

2 \underset{- \frac{π}{4}}{\int^{\frac{3 π}{4}}} (\sin x + \cos x) dx =

2 {[- \cos x + \sin x]}_{- \frac{π}{4}}^{\frac{3 π}{4}} =

2 {\sqrt{2} - (- \sqrt{2})} = 4 \sqrt{2}