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If `I(m) = int_0^pi ln(1-2m cos x + m^2)dx`, then I(1)= |
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Answer» Correct Answer - 6 `I=lim_(nto oo) (pi)/n [In (a^(2)-2acos (pi)/n+1)+In(a^(2)-2a cos (pi)/n+1)……..+ In (a^(2)-2a cos ((n-1)pi)/n+1)]` `=lim_(nto oo) (pi)/n In (a^(2)-2a"cos"(pi)/n +1)(a^(2)-2a"cos"(2pi)/n +1)…….(a^(2)-2a"cos"((n-1)pi)/n)+1)` `= lim_(nto oo) prod_(k=1)^(n-1)(a-e^((ikpi)/n))(a-e^((-ikpi)/n))=lim_(nto oo) prod ((a^(2n)-1)/(a^(2)-1))^(1/n)=2piIna` |
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