Question

Show that 0òp q3 ln sin q dq = 3p/2 0òp q2 ln [Ö2 sin q] dq.

Joshi sir comment

 let I = 0òp q ln sin q dq

on aplying property of definite integral

I =  0òp (π-q) ln sin q dq

so 2 I =  0òp π ln sin q dq 

or I = π/2  0ò ln sin q dq


or I = 2π/2  0òp/2 ln sin q dq    this is due to property

similarly solve  0òp q2 ln sin q dq  and   then 0òp q3 ln sin q d


finally solve the right hand side of the equation to prove LHS = RHS

 

 

Submit Your Answer


please login to submit your answer

Login Here

Register