Integral or differential

Calculus Level 4

For a real number \(x > 0\), let \[\large F(x) = \int_{x^2}^{4x^2} \sin\sqrt t\, dt\]

For a real number \(t > 0\), let \(\sqrt t\) denote the positive square root of \(t\). If \(F'\) is the first derivative of \(F\), find the value of \(F'\left(\dfrac{\pi}{2}\right)\)?

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