WBJEE2018MathematicsIndefinite IntegrationActual

If f(x) x x d x= 1 2 (b²-a² ) f(x)+c where c is the constant of integration, then f(x) is equal to

Correct answer

Step-by-step solution

We have. f(x) x x d x= 1 2 b²-a² (f(x))+c f(x) x x= 1 .2 b²-a² ) 1 f(x) f'(x) f(x) 2 x= 1 b²-a² f'(x) f(x) 2 x= 1 b²-a² f(x) (f(x))² 2 x d x= 1 b²-a² f(x) (f(x))² d x - 2 x 2 = 1 b²-a² ( -1 f(x) ) 2 x (b²-a² ) 2 = 1 f(x) f(x)= 2 (b²-a² ) 2 x

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