InterviewSolution
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(iii)सिद्ध करे कि , ` int _(0)^(1) tan^(-1). ((2x-1)/(1+x-x^(2)))dx = 0` |
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Answer» ` tan^(-1) ((2x-1)/(1+x-x^(2))) = tan^(-1).(x-(1-x))/(1+x(1-x)) = tan^(-1) x - tan^(-1) (1-x)` माना कि ` I = int _(0)^(1) [ tan^(-1) x - tan^(-1) (1-x) ] dx ` तो, ` I = int _(0)^(1) [ tan^(-1) (1-x) - tan^(-1) x ] dx " " :. 2I = 0 rArr I = 0 ` |
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