InterviewSolution
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InterviewSolution
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सिद्ध कीजिये - `int_(0)^(oo)log(x+(1)/(x))(dx)/(1+x^(2))=pi log2` |
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Answer» माना ` x = tan t rArr t = tan^(-1) x rArr dt=(1)/(1+x^(2))dx` तब `" "I=int_(0)^(oo)log(x+(1)/(x))(dx)/(1+x^(2))=int_(0)^(pi//2)log(tant+(1)/(tant))dt` `=int_(0)^(pi//2)log((1)/(sin t cost))dt` `=int_(0)^(pi//2)(log 1-log sin t-log cos t)dt` `=- int_(0)^(pi//2)log sin t dt-int_(0)^(pi//2)log cos tdt` |
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