using graph to find work done

Question

(asked this question but the method didn't get me to the correct answer)

The graph shows the x component of a force that acts on an object that moves on the x axis. The vertical spacing between adjacent grid lines is 5.06 N, while the horizontal spacing between adjacent grid lines is 1.0 m.

if you search this question you will find the image of the graph i am unable to insert an image here

What is the work done by the force, in joules, as the object moves from x = 4 m to x = 6 m?

i thought you would set up an integral and then solve but it keeps telling my answer is incorrect.

Answer 1

If I am looking at the right picture (this one https://media.cheggcdn.com/media/d0c/d0c1cad6-c2b6-4ec5-9aca-60d2aaa2fcfc/phpEdCySJ.png), it looks like the y-intercept is at 4 gridlines up, and has a slope of -3/4. The equation for the line would be y=-3x/4 + 4. Since this is a linear equation an integral is a little bit heavy-handed here, but I'll roll with it.

6 6

∫ (-3/4)x + 4 dx = (-3/8)x² + 4x|

4 4

= (-108/8 + 24) - (-48/8 + 16) = (-13.5 + 24) - (-6 + 16) = 10.5 - 10 = 0.5

This is not the answer though, since the y-axis isn't in Newtons. To get the y-axis to be in Newtons, we have to vertically stretch the equation of the line by 5.06 which equates to multiplying our final answer by 5.06, since we can pull it out of the integral. Thus, the final answer is 5.06*0.5 = 2.53 N.