 # how can i integrate log sinx  from 0 to pi/2 . plz give full stepwise solution 13 years ago

Dude do integration by parts.....................u=1 and v=f(x) then properly substitute sinx if reqd.............. Badiuddin askIITians.ismu Expert
148 Points
13 years ago

Dear Bharat

Let I =limit  o to pi/2  ∫ log sinx dx ....................1

use property

I= limit 0 to pi     ∫log sin(pi/2 -x) dx

or

I =

I= limit 0 to pi/2     ∫log cos(x) dx..................2

1+2

2I =limit 0 to pi /2    ∫log sinxcos(x) dx

2I =limit 0 to pi/2     ∫log (sin2x)/2  dx

2I =limit 0 to pi/2     ∫log sin2x dx   -  limit 0 to pi/2 log2 dx

2I =limit 0 to pi /2    ∫log sin2x dx   -  pi/2*log2........................3 =

let I1=imit 0 to pi/2     ∫log sin2x dx

2x=t

2dx=dt

I1=imit 0 to ∏     1/2∫log sint dt

use property

I1=imit 0 to ∏/2     2*1/2∫log sint dt

I1=imit 0 to ∏/2     log sint dt    =I

put this in equation 3

2I=I -/2  log2

I=-/2 log2

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.

All the best.

Regards,