Evaluate line segment C from P to Q

[Phil Frehz]

Homework Statement

Evaluate ∫_C F⋅dr along the line segment C from P to Q

F(x,y) = 8 i + 8 j ; P (-4,4) , Q (-4,5)

Homework Equations

The Attempt at a Solution

I believe I got most of the work done but I am have trouble finding the limits of the curve.

What I have done was create a vector v=PQ= <0,1>. I then made the parametric equations:

x = -4
y= 4 + t

I then derived x & y to get a dr(t) = dt j

F dot dr gives me 8dt... combining everything I get ∫_C 8dt.

To find the limits of C I plugged Q into the parametric equations to give me values of t which were 0 & 1.

Attached is my work to clarify, not sure if correct.

 

[ehild]

Your result is correct, but you do not need to integrate, as it is a constant force.