Suppose that for real numbers $p_1$, $p_2$, ..., $p_{15}$ we have $\sum _{k=1}^{15}{p}_k=30$. What is the value of $\sum _{k=1}^{15}\frac{p_k}{6}$?

The graph of $h\left(x\right)$ is given below. Compute ${\int }_0^{3}h\left(x\right)dx$ using geometry.

An $8\text{ cm}$ solid cylinder has a density that varies along its length according to the function shown in the figure below. What is the mass of the segment from $x=0$ to $x=8$? Note: The density is measured in $\text{g/cm}$.

A car traveling along a straight road has a velocity in $\text{m}/\text{s}$ represented by the graph of $v=f\left(t\right)$ on the interval $0\le t\le 12$, as shown. The time $t$ is in seconds. Divide $[0,12]$ into $n=2$ subintervals: $[0,6]$ and $[6,12]$. Estimate the displacement of the car on $[0,12]$ by assuming that the car travels at a constant velocity equal to the value of $v$ evaluated at the midpoint of each subinterval.