IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

gayathri

_{[ ]}

^{[ ]}sin^3x.cos^5x dx

in this sum , if we use ILATE rule which should we give preferencefor sin or cos??

aditya_arora04

Are yaar !!!

You don't need ILATE.

Look,

Write it as :

sin²x.cos⁵x.sinx dx

put t = cosx

So, -dt = sinx.dx

So,

(1-t²)t⁵dt

open it up and you get the answer.

Got it ?????

umang

Hey aditya !

This is indeed a gr8 solution .

But , I think , if we do by ILATE rule , then anyone can be taken first .

what do u say , aditya ???

aditya_arora04

Yes, but it would be better to take cos^3x as second function because it would be relatively easier to solve.

But, yes both can be given preference.

puneet

hiii

well, ILATE is just a rule which is to help people solve questions. It is not a theorem ... this is very important ...

There is nothing like u have to follow it .. Just see how the question can be solved and take first and second function accordingly.

I am emphaising on this point strongly because in my opinion this is important that people understand and do not remain in the shell of that rule .. there are occasions when the ILATE might not work .. so just try to solve the problem .. and that is the best way to go about ..

cheers

ruhi

hi gayathri i think if u use "by parts" in dis question then it will b tedious......aditya's soln is perfect.........always remember ilate cant b applied newhere.......by parts is aaplied only where the question can b reduced in a form where one part is easy to integrate nd the other is easy to differentiate
nw in dis case if u apply ilate prefernce can b given to neone....but u ve to reduce sin^3 x or cos^5 x in a form dat can b integrated.....nd it will bcum unnecessary lengthy..........sooo....where 2 use wot depends on the question.....i hope u r getting wot i wanna say
thanx

Ask & Discuss Questions with Community & Experts