4)Encuentre las dimensiones del cilindro circular recto con volumen máximo que puede inscribirse en un cono circular recto de 8 pulgadas de radio y 12 pulgadas de altura

Question Given \( f(x) \) below, find \( f^{\prime}(x) \) \[ f(x)=\int_{\sqrt{x}}^{x^{3}} t^{4} d t \]

\begin{tabular}{l} Question \\ Given \( F(x) \) below, find \( F^{\prime}(x) \). \( F(x)=\int_{x}^{5} \sqrt{2 t-2} d t \) \\ Provide your answer below: \\ \hline\( F^{\prime}(x)=\square \)\end{tabular}

Question Given \( f(x) \) below, find \( f^{\prime}(x) \). \[ f(x)=\int_{4 x}^{x^{3}}\left(t^{3}-11\right)^{7} d t \]

Question Given \( F(x) \) below, find \( F^{\prime}(x) \) \[ F(x)=\int_{2}^{e^{x}}\left(t^{3}+8\right) d t \]

Question Given \( F(x) \) below, find \( F^{\prime}(x) \). \[ F(x)=\int_{3}^{x} e^{t^{3}-10} d t \]