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Dinesh Gupta Grade: 12
        

[f ( x )]101    =


        1 + ∫0xf(t) dt


 [ f (100)]101     =?

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear DInesh



[f ( x )]101    =        1 + ∫0xf(t) dt


differentiate


101[f ( x )]100 f'(x) =f(x)


101[f ( x )]99 f'(x) =1


now integrate


101 [f ( x )]99 f'(x)dx =∫dx


101/100 [f ( x )]100  =x +c


at x=0      f(x) =1 from given relation


so value of c is 101/100


so 

101/100 [f ( x )]100  =x +101/100


                  [f ( x )]100    =100/101 x +1


 


or   [f ( x )]101    =[100/101 x +1]101/100








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Badiuddin


   


7 years ago
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