Do you even integrate bro?

Calculus Level 5

A positive, real valued, continuously differentiable function ff satisfies the following equation, [f(x)]2=0x((f(t))2+(f(t))2)dt+e2.\large [f(x)]^2= \int^x_0 ( (f(t))^2+(f'(t))^2) \,dt +e^2.

Find f(1) f(1) .

Give your answer to 3 decimal places.

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