1.

(iii)सिद्ध करे कि , ` int _(0)^(1) tan^(-1). ((2x-1)/(1+x-x^(2)))dx = 0`

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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