 #1
Ark236
 17
 2
 Homework Statement:

Hi everyone.
I was studying an example of Kleppner's book and I have a question.
In this example, the path integral is calculated, starting from the point (0,0) and going to the point (0,1). The force is $$F = A(xy \hat{i}+ y^2 \hat{j})$$. The path followed is denoted by (a,b,c) (see figure).
 Relevant Equations:
 $$W = \vec{F}\cdot \vec{dr}$$
In the book it is mentioned that, in path c, the line integral would be:
$$\int \vec{F}\cdot \vec{dr} = A \int_{1}^{0}xy dx = A\int_1^0 x dx = \dfrac{A}{2}$$.
but I think that dx is negative in that case, the result would be positive, right?
$$\int \vec{F}\cdot \vec{dr} = A \int_{1}^{0}xy dx = A\int_1^0 x dx = \dfrac{A}{2}$$.
but I think that dx is negative in that case, the result would be positive, right?