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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





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