Question Number 100216 by Rio Michael last updated on 25/Jun/20

if I = ∫_0 ^(π/2) ((sin x)/(sin x + cos x))dx = ∫_0 ^(π/2) ((cos x)/(sin x +cos x))dx then I = ??

Commented byDwaipayan Shikari last updated on 25/Jun/20

(π/4) (I think it should be)

Commented byDwaipayan Shikari last updated on 25/Jun/20

∫_0 ^(π/2) ((sinx)/(sinx+cosx))dx=∫_0 ^(π/2) ((sin((π/2)−x))/(sin((π/2)−x)+cos((π/2)−x)))dx=∫_0 ^(π/2) ((cosx)/(sinx+cosx))dx=I so, 2I=∫_0 ^(π/2) ((sinx+cosx)/(sinx+cosx))dx=(π/2) So, I=(π/4)

Answered by Ar Brandon last updated on 25/Jun/20

{ ((I=∫_0 ^(π/2) ((sinx)/(sinx+cosx))dx..........(1))),((I=∫_0 ^(π/2) ((cosx)/(sinx+cosx))dx...........(2))) :}⇒I+I=∫_0 ^(π/2) ((sinx+cosx)/(sinx+cosx))dx ⇒2I=∫_0 ^(π/2) dx=(π/2)⇒I=(π/4)

Commented byCoronavirus last updated on 25/Jun/20

clean

Commented byAr Brandon last updated on 25/Jun/20

Ouais

Commented byRio Michael last updated on 26/Jun/20

thank you′ll