Let's do some derivative #2

Calculus Level 2

\[ \large \int_0^{x^2} (1+t) f(t) \, dt = 6x^4 \]

Find a real valued function \(f\) defined and continuous for \(x\ge 0\) such that the equation above is true. Submit your answer as the value of \(f(1) \).

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