Question

integration question

Answer 1

http://gyazo.com/cc36b94b6a16a2de5bd91af9698ad018

Answer 2

how do i start?

Answer 3

substitute y=a-x
\[I= \int\limits_{a}^{0}\frac{ f(a-x) }{ f(a-x)+f(x)}*-dx \rightarrow I= \int\limits_{0}^{a}\frac{ (f(a-x) }{ f(a-x)+f(x) }\]

Answer 4

you can add the two integrals to get:
\[2I=\lim_{0 \rightarrow a}\frac{ f(x)+f(a-x) }{ f(x)+f(a-x) }= a\] solve I to get \[I=\frac{ a }{ 2 }\rightarrow \int\limits_{0}^{a}\frac{ f(x) }{ f(a-x)+f(x) }=\frac{ a }{ 2 }\]

Answer 5

i.dont.get.it.sorry!

you said substitute \(y=a-x\)? it doesnt make sense..

Answer 6

dude I just wanna notify you that after substitution y=a-x you will get the same integral in terms of y, so just change y to x cause it's just a symbol...

Answer 7

did that make sense now?

Answer 8

i dont get the change of limits in the first integral you wrote from \(0\) to \(2\)?

Answer 9

i mean \(0\) to \(a\)?

Answer 10

a-0 =a
a-a=0

Answer 11

and also I'm sorry about the limit, I mean integral..

Answer 12

meant**

Answer 13

Oh i got it now, thank youu!!!

Answer 14

you are welcome :)