Find the area bounded by the graphs of the indicated equations over the given interval. \[ y=-x^{2}+29 ; y=0 ;-3 \leq x \leq 3 \] The area is \( \square \) square units.

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

Question Given \( F(x) \) below, find \( F^{\prime}(x) \). \[ F(x)=\int_{1}^{2 x^{2}} \frac{t}{t-1} d t \]

A company manufactures and sells \( x \) clocks per week with weekly price-demand function: \( f(p)=30-3 p \) where \( p \) is the price per clock. a. Compute the elasticity of demand function, \( E(p) \), for this demand function. \( E(p)= \) b. At \( p=3 \), a price increase of \( 2 \% \) will create a demand decrease of what percent? Round to 2 decimal places if necessary.

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