a-b-f-x-f-x-f-a-b-x-dx-

Question Number 118395 by TANMAY PANACEA last updated on 17/Oct/20

\int_{a}^{b} \frac{f (x)}{f (x) + f (a + b - x)} d x

Commented by Dwaipayan Shikari last updated on 17/Oct/20

\frac{b - a}{2}

Commented by TANMAY PANACEA last updated on 17/Oct/20

t h a n k y o u \dots d u r g a p u j o h o c h h e

Commented by Dwaipayan Shikari last updated on 17/Oct/20

F r o m 23 o c t

Commented by Dwaipayan Shikari last updated on 17/Oct/20

A r e y o u i n K o l k a t a s i r ?

Commented by TANMAY PANACEA last updated on 17/Oct/20

n a a m i n a g p u r a . .

Answered by mathmax by abdo last updated on 17/Oct/20

I = \int_{a}^{b} \frac{f (x)}{f (x) + f (a + b - x)} dx we do the changement a + b - x = t \Rightarrow

I = \int_{b}^{a} \frac{f (a + b - t)}{f (a + b - t) + f (t)} (- dt) = \int_{a}^{b} \frac{f (a + b - x)}{f (a + b - x) + f (x)} dx \Rightarrow

2 I = \int_{a}^{b} \frac{f (x) + f (a + b - x)}{f (a + b - x) + f (x)} dx = \int_{a}^{b} dx = b - a \Rightarrow I = \frac{b - a}{2}

Commented by TANMAY PANACEA last updated on 17/Oct/20

t h a n k y o u s i r

Commented by Bird last updated on 17/Oct/20

y o u s t i l l w o r k a t r a i l w a y s s i r t a n m a y . .

Commented by TANMAY PANACEA last updated on 17/Oct/20

y e s s i r t i l l b e c o m e s e n i o r c i t i z e n i n y e a r 2030

Commented by mathmax by abdo last updated on 17/Oct/20

good luck sir tanmay

Answered by TANMAY PANACEA last updated on 17/Oct/20

f o r m u l a

\int_{q}^{p} f (x) d x = \int_{q}^{p} f (p + q - x) d x

I = \int_{a}^{b} \frac{f (x)}{f (x) + f (a + b - x)} d x

= \int_{a}^{b} \frac{f (a + b - x)}{f (a + b - x) + f {(a + b - (a + b - x)}} d x

= \int_{a}^{b} \frac{f (a + b - x)}{f (a + b - x) + f (x)} d x

2 I = \int_{a}^{b} d x

I = \frac{b - a}{2}

Commented by bramlexs22 last updated on 17/Oct/20

t h i s i s f o r m u l a K i n g I n t e g r a l s i r ?