Suppose $g$ is continuous on $[2,5]$ and ${\int }_2^5\mid g\left(x\right)\mid dx=0$ Which of the following must be true?

Given the velocity-time graph of a car moving along a straight road for $t\in [0,10]$, what is the displacement of the particle between $t=0$ and $t=3$ ?

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 $x=4$? 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.

Suppose $\sum _{k=1}^{12}{x}_k=18$ and $\sum _{k=1}^{12}{y}_k=-7$. Compute the value of $\sum _{k=1}^{12}(x_k-y_k+3)$.