Do you even integrate bro?

Calculus Level 5

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

Find \( f(1) \).

Give your answer to 3 decimal places.

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