\begin{tabular}{l} (1) \( f(x)=3 x^{3}+2 x^{2}-5 x-10 \) \\ a) \( \int_{3}^{8} f(b)-f(a)= \) \\ b) Derivada \\ c) Velocidad \( \quad{ }_{m}=\frac{f\left(x_{i}\right)-f(x i)}{x_{f}-x_{i}} \quad[3,5] \) \\ \hline\end{tabular}

Suppose \( \int_{2}^{4} f(x) d x=6, \int_{2}^{7} f(x) d x=-2 \), and \( \int_{2}^{7} g(x) d x=4 \). Evaluate the following integrals. (Simplify your answer.) 7 \( \int_{2} 5 g(x) d x=20 \) (Simplify your answer.) 7 \( \int[g(x)-f(x)] d x=6 \) 2 \( (S i m p l i f y \) 7 \( \int_{2}^{7}[5 g(x)-f(x)] d x=\square \) 2

Suppose \( \int_{2}^{4} f(x) d x=6, \int_{2}^{7} f(x) d x=-2 \), and \( \int_{2}^{7} g(x) d x=4 \). Evaluate the following integrals. \( \int_{7}^{2} g(x) d x=-4 \) (Simplify your answer.) \( \int_{7}^{7} 5 g(x) d x=20 \) 2 (Simplify your answer.) \( \int_{7}^{7}[g(x)-f(x)] d x=\square \) 2 (Simplify your answer.)

\( \int_{2}^{7} 5 g(x) d x=\square \) (Simplify your answer.)

What is the average rate of change on the function \( f(x)=x^{2} \) between \( x= \) 1 and \( x=3 \) ? -1

Suppose \( \int_{2}^{4} f(x) d x=6, \int_{2}^{7} f(x) d x=-2 \), and \( \int_{2}^{7} g(x) d x=4 \). Evaluate the following integrals. \( \int_{7}^{2} g(x) d x=-4 \) (Simplify your answer.) \( \int_{2}^{7} 5 g(x) d x=\square \) (Simplify your answer.)