InterviewSolution
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InterviewSolution
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Prove:`int_0^(pi//2) log|tanx| dx=0` |
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Answer» Let `I=int_(0)^(pi//2)log(tanx)dx`…….`(i)` Then, `I=int_(0)^(pi//2)log[tan((pi)/(2)-x)]dx` `[:.int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx]` or `I=int_(0)^(pi//2)log(cotx)dx=int_(0)^(pi//2)log((1)/(tanx))dx=-int_(0)^(pi//2)logtanxdx=-I`. `:.I=-I` or `2I=0` or `I=0`. Hence, `int_(0)^(pi//2)log(tanx)dx=0`. |
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