# Mother of All Calculus!

Calculus Level 4

If a positive real valued continuously differentiable functions $$f$$ on the real line such that for all $$x$$

$\large\ f^{ 2 }\left( x \right) = \int _{ 0 }^{ x }{ \left( { \left( f\left( t \right) \right) }^{ 2 } + { \left( f'\left( t \right) \right) }^{ 2 } \right) dt } + { e }^{ 2 }$

is satisfied.

Then find the value of $$\large\ f(-1)$$.

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