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

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Grade 12Differential Calculus

[f ( x )]¹⁰¹ =

1 + ∫₀^xf(t) dt

[ f (100)]¹⁰¹ =?

Dinesh Gupta

16 Years agoGrade 12

1 Answer

Badiuddin askIITians.ismu Expert

16 Years ago

Dear DInesh

[f ( x )]¹⁰¹ = 1 + ∫₀^xf(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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