If $f(x)=\int_0^x\{f(t)\}^{-1} d t$, and $\int_0^1\{f(t)\}^{-1} d t=\sqrt{2}$, then $f(x)=$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f(x)=\int_0^x\{f(t)\}^{-1} d t

, and

\int_0^1\{f(t)\}^{-1} d t=\sqrt{2}

, then

f(x)=

View answer and explanation

Correct option: A

\sqrt{2 x}

Option D (28/3) is correct because it involves splitting the integral into intervals where

|1-x^2|

is either

(1-x^2)

(x^2-1)

, then integrating and summing the results.

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