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bharat bhushan sharma Grade: Upto college level
`        how can i integrate log sinx  from 0 to pi/2 . plz give full stepwise solution`
7 years ago

Answers : (3)

manas pawar
23 Points
```										Dude do integration by parts.....................u=1 and v=f(x) then properly substitute sinx if reqd..............
```
7 years ago
Badiuddin askIITians.ismu Expert
147 Points
```										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. We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.  All the best.  Regards, Askiitians Experts Badiuddin

```
7 years ago
Sudipto Koley
32 Points
```										∫(a+b sin x) / (b+a sin x) dx
```
2 years ago
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