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[f ( x )] 101 = 1 + ∫ 0 x f(t) dt [ f (100)] 101 =?

[f ( x )]101    =


        1 + ∫0xf(t) dt


 [ f (100)]101     =?

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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

   

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