IIT JEE , AIEEE Forum - Mathematics , Integral Calculus - inte of {(sinx)^1/n /(sinx)^1/n+(cosx)^1/n}dx..pls help me experts..!!(its not def int q)!

ackhill

inte of {(sinx)^1/n /(sinx)^1/n+(cosx)^1/n}dx..pls help me experts..!!

hsbhatt

Is it a definite integral by any chance?

puneet

hii

well yeah .. shud be a definite intergral ..

cheers

ackhill

no pls yaar!..its not a definite int q!...it wud so easy den!!...pls give me d sol..pls experts help!..

ackhill

hey goiitians help me pls!!!..

digs2digi

hey dont u have the options with u??
if yes then v cud have put the vlues of n(i,2,3...)
and compared!!!!!!!111

ackhill

no man!..sorry...but i`ve tried dis q a lot!..pls try it na!..

ackhill

pls solve dis na...if n=1/2..(atleast dis 1)

akhil_o

if its half then it is same as

int (sin^2 x/ sin^2 x + cos ^2 x)
=int (sin ^2 x)
=int (1- cos2x)/2
= x/2 -sin 2 x/4

aankurverma

answer is pi/4 n d questions is integral of 0 to pi/2

I = _{[ 0]}

^{[ pi/2]} sinx^1/n/(sinx^1/n + cosx^1/n)
2I = _{[ 0]}

[ pi/2]dx
I = pi/4

ackhill

@ankur,its not an def int sum...i`ve clearly written it..
@ akhil,no yaar it cant b d same..even if u rationalize it we get stuck in between...
but neways i`ve found out d ans.
first we divide it by root sinx and then proceed
we get in deno. 1+root (cotx)...
after its easy now...

akhil_o

all i did was solve for n=1/2 as u asked!
i didnt generalise

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