Question

integral of (-cosx)/(cosx+sinx) from 0 to pi/2 .. !!! Please explain me how to do this the easiest way =)

Answer 1

There's an identity in there somewhere..

Answer 2

try do rationalization.

Answer 3

what do you mean ? i don't think we learned it yet ..

Answer 4

Disregard.

Answer 5

lol you did it wrong

Answer 6

just for checking

u doin integral for [0 to pi/2] or [-pi/2 to pi/2]?

Answer 7

i will tell you, the answer should be pi/4 and i know that somehow you can write the integral as 2*integral of (cosx +sinx)/(cosx+sinx) but i don't understand why ... =(

Answer 8

from 0 !!! sorry !

Answer 9

cause the differential of denominator is present in in numerator

Answer 10

ok so what we have is\[\int_{0}^{\pi/2} \frac{\cos x}{\cos x+\sin x} \text{d}x\]

Answer 11

yup mukushla

Answer 12

i got it!

Answer 13

take cos x common from both numerator and denominator

Answer 14

i guess so it will be easier that way cause the final eq will be
\[\int\limits_{?}^{?}1/(1+tanx)\]

Answer 15

\[I=\int_{0}^{\pi/2} \frac{\cos x}{\cos x+\sin x} \text{d}x\]TT will show us that with sub \(x=\frac{\pi}{2}-x\) we have \[I=\int_{0}^{\pi/2} \frac{\sin x}{\cos x+\sin x} \text{d}x\]

Answer 16

haha no I won't :)

Answer 17

lol

Answer 18

so you did \[u=\pi/2-x\]?

Answer 19

hmmm wait a minute .. you should replace the limits as well no ?

Answer 20

that's what I was gonna say

Answer 21

\[-\int_{\pi/2}^0{\sin u\over\sin u+\cos u}du\]?

Answer 22

which is what you wrote, ic :P

Answer 23

and\[-\int_{\pi/2}^0{\sin u\over\sin u+\cos u}du=\int_{0}^{\pi/2}{\sin u\over\sin u+\cos u}du\]

Answer 24

right, I get it now...

Answer 25

that integral seems no easier to me though

Answer 26

how can i continue? i can't add them together because of the different integrands =\

Answer 27

\[I=\int_{0}^{\pi/2}{\cos x\over\sin x+\cos x}dx=\int_{0}^{\pi/2}{\sin x\over\sin x+\cos x}dx\]\[2I=\int_{0}^{\pi/2}{\sin x+\cos x\over\sin x+\cos x}dx=\int_{0}^{\pi/2}1dx\]

Answer 28

ohhh i get it !! thanks a-lot to both of you !!!! =)

Answer 29

that is sweet dude!

Answer 30

:)