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# CBSE Class 12-science Answered

evaluate integration of log(sinx) dx
Asked by jprathamesh023 | 23 Mar, 2024, 04:01: PM
Expert Answer

Let us use the following property of definie integration ,

Then eqn(1) becomes

By adding (1) and (2) , we get

Let us use the substitution u = 2x  ;  du = 2 dx ;

when x = 0 , u = 0 ; when x = π/2 , u = π ;

Now let us use the following property of definite integration

Using the above property integration I1 is

above integration is written because  log(sin(π-u)) = log(sinu)

RHS of above expression is same as I as given in eqn.(1).

Hence I1 = I

Then from eqn.(3) , we get

I = - log2 ( π/2)

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Answered by Thiyagarajan K | 23 Mar, 2024, 09:21: PM

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