Question

Let C be the curve which is the union of two line segments, the first going from (0, 0) to (4, -3) and the second going from (4, -3) to (8, 0).
Compute the line integral of int(4dy+3dx)

Answer 1

∫4dy  + 3dx

You can do this using Green's theorem. The line integral over the boundary of the closed triangle.
See the partial derivative of the partial derivative of 3 with respect to y = 0

You can see that now the line integral can be divided into three sides of triangle

hope this helps