\( \int_{0}^{5} f(x) d x \), where \( f(x)=\left\{\begin{array}{ll}5 & \text { if } x \leq 3 \\ 3 x-4 & \text { if } x>3\end{array}\right. \)

A factory selling cell phones has a marginal cost function \( C(x)=0.01 x^{2}-3 x+229 \), where \( x \) represents the number of cell phones, and a marginal revenue function given by \( R(x)=429-2 x \). Find the area between the graphs of these curves and \( x=0 \).

d) \( f(x)=-\frac{3}{s^{2}}-\frac{4}{s^{4}} \) a. \( 6 s^{-3}+16 s^{-5} \) b. \( 16 x^{4}+2 x \)

Set up the definite integral required to find the area of the region between the graph of \( y=13-x^{2} \) and \( y=24 x+148 \) over the interval \( -5 \leq x \leq 3 \).

Realiza la investigación encome Integrar: de resolver los ejercicios: 1. \( \int x^{3} \cdot e^{x} d x \) 2. \( \int|1-x| \cdot \sqrt{x} d x \) 3. \( \int \frac{3 x}{\sqrt[3]{x^{2}+3}} d x \)

\( \int \sqrt[ \infty ] { x ^ { r } } d x \)