### Home > APCALC > Chapter 5 > Lesson 5.5.1 > Problem5-161

5-161.

​ Examine the equation $x ( 1 ) + \int _ { 1 } ^ { 7 } v ( t ) d t = 22$ where $v$ represents the velocity of a particle moving along the $x$-axis on a sheet of centimeter grid paper in cm/sec. At $t=1$, the particle is at the point $(7,0)$.

1. Write a complete description about what the integral $\int _ { 1 } ^ { 7 } v ( t ) d t$ is computing. Use correct units and be sure to mention the meaning of the bounds in your description.

What does the integral of velocity represent?

2. In the context of the problem, what does the value $22$ represent?

$x\left(1\right)$ represents the position of the particle at $t=1$. Add this to the integral which you described in part (a), and the sum is $22$.

3. Evaluate $\int _ { 1 } ^ { 7 } v ( t ) d t$.

According to the last sentence of the problem, $x(1)=7$.