Chapter 6, Problem 7RCC

To determine

What ${\displaystyle {\int }_0^{6}f\left(x\right)dx}$ represents and the units for integral.

Answer to Problem 7RCC

  ${\displaystyle {\int }_0^{6}f\left(x\right)dx}$ represents the work done by me to push the book across a $6m$ long table.

The unit for integral is Joule.

Explanation of Solution

Given information :

  $f\left(x\right)$ is the force excreted at points $x$ .

The length of the table is $6m$ .

  $f\left(x\right)$ is measured in Newton.

Formula used :

  $\text{work = Force }\times \text{ Displacement of the point of action}\text{.}$

Here $f\left(x\right)$ is the force and $dx$ is the displacement.

So, $f\left(x\right)dx$ is work.

Here, ${\displaystyle {\int }_0^{6}f\left(x\right)dx}$ represents total work done i.e. work done for pushing the book from $0m$ to $6m$ .

As the unit of $f\left(x\right)$ is Newton and the $dx$ is in $m$ ; the operation is done in SI system.

Hence the unit of work will be Joule.