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Integral Calculus

Blazing goIITian

Joined:	11 Jun 2007
Post:	914

20 Sep 2007 07:49:52 IST

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543

indefinite integral Q

None

slove ^{_{dx/(x + 1-x)}}

_{^{plz solve this q (source TMH)}}

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Comments (3)

Neeraj Agarwal

Blazing goIITian

Joined: 22 Jan 2007

Posts: 2039

20 Sep 2007 17:58:29 IST

Like 1 people liked this

rationalize.....!!

joy francis

Blazing goIITian

Joined: 19 Feb 2007

Posts: 1802

21 Sep 2007 10:13:53 IST

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Hi.

Rationalize first..you will get.

I = (rootx - root(1-x)) / 2x-1

=rootx / 2x-1 - root(1-x)/2x-1

for the first part take x = t^2

so , the integral becomes

2t²dt / 2t²-1

= 1 + 1/2t²-1

now use std results

...similarly do for second part by taking 1-x = t^2

RAKESH KUMAR

Cool goIITian

Joined: 24 Mar 2007

Posts: 39

8 Nov 2007 13:11:44 IST

Like 2 people liked this

HI DEAR,

YOUR QUESTION IS dx/[x + (1-x)]

PUT x = (sin^2(t))

i.e. dx = sin2t dt

THEN WE GET sin2t dt/(sint + cost)

NOW sin2t(cost - sint) dt/ cos2t

i.e. tan2t(cost - sint) dt

NOW I THINK YOU WILL BE ABLE TO SOLVE THIS QUESTION

BY USING THE PRODUCT RULE

PLEASE RATE...................IF SATISFIED........................................................

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