\( \frac { d y } { d x } = \frac { t } { x e ^ { a + 2 x } } \)

\begin{tabular}{|l|}\hline 2. Calcula el volumen \\ del sólido de \\ revolución que se \\ forma de girar sobre \\ el eje \( x \) la función \\ \( f(x)=x^{2}+x \) con \\ límites \( [-1,5] \)\end{tabular}

Calcule el limite de \( y=x^{2}+x-6 \) \( \lim _{x \rightarrow 3} \frac{x^{2}+x-6}{x+3} \)

(10 points) Use the Fundamental Theorem of Calculus to find the exact values of the definite integral. \( \int_{1}^{3} 3\left(2^{x}\right) d x= \)

\begin{tabular}{|l|}\hline 3. \( \begin{array}{l}\text { Calcula el volumen } \\ \text { del sólido de } \\ \text { revolución que se } \\ \text { forma de girar sobre } \\ \text { el eje } x \text { las funciones } \\ f(x)=2 x^{2}+\frac{1}{2} y \\ g(x)=x \text { con límites } \\ {[0,3]}\end{array} \) \\ \hline\end{tabular}

38. Use integration formulas to solve each integral. You may have to use algebra, educated guess-and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. (a) (10 points) \( \int\left(x^{2}-3 x^{8}-7\right) d x= \) (b) (10 points) \( \int 3 \cos (x) d x= \) (c) (10 points) \( \int x^{2}\left(x^{3}+1\right) d x= \)