Calculate electric potential from a graph

[jlmccart03]

Homework Statement

A region of space has a non-uniform electric field that points in the +x-direction and has magnitude as shown in the figure (Figure 1) As a reference point, take the potential at the origin to be -140 V .
Calculate the electric potential at x=3.0m.
Express your answer to two significant figures and include the appropriate units.

Homework Equations

-∫E⋅dr
Ex = -dV/dx

The Attempt at a Solution

So I attempted to take the integral from 0 to 3 of the graph seen, but I did not know what E and dr were. I searched the web and found the closes thing being the potential difference given at x = 0. This is where I got lost and could not figure out what I needed to put in for dr and E fully. I know I have to integrate somehow, but with what? I just know the boundaries are 0 to 3, but everything else is confusion.

P.S. Also is there any really good physics 2 textbooks that explain these concepts very well? I know of the Feynman lectures, but any old school physics books that could be recommended for elctrostatics and such. Thanks to any suggestions!

 

[haruspex]

So I attempted to take the integral from 0 to 3 of the graph seen,

Two ways to approach this.
One way is to use the given graph of E against x to write E as an algebraic function of x. This will be in two parts, one for x from 0 to 2 and one for x from 2 to 3. When you have done that you can integrate.
The easier way comes from understanding the relationship between areas and integrals.

 

[scottdave]

Finding the area under the the graph is the same as integrating. Find the area between two distances, gives the voltage difference between those two positions. So you know the starting voltage, and you can find the voltage difference (the area of a rectangle and a triangle) then you can calculate the voltage at 3 meters.