Integral or differential

Calculus Level 4

For a real number x>0x > 0, let F(x)=x24x2sintdt\large F(x) = \int_{x^2}^{4x^2} \sin\sqrt t\, dt

For a real number t>0t > 0, let t\sqrt t denote the positive square root of tt. If FF' is the first derivative of FF, find the value of F(π2)F'\left(\dfrac{\pi}{2}\right)?

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