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).

Computer the line integral ∫(-4dy -3dx)

Answer 1

To compute the line integral ∫(-4dy -3dx) over the curve C, we break it into two parts and evaluate it separately for each line segment. The first segment gives a value of 0 and the second segment gives a value of -4.

Step-by-step explanation:

The line integral ∫(-4dy -3dx) can be evaluated by breaking it into two parts: one over the line segment from (0,0) to (-4,3) and the second over the line segment from (-4,3) to (-8,0).

For the first line segment, we have ∫(-4dy -3dx) = ∫(-4dy) - ∫(3dx). Evaluating these integrals gives -4(3-0) - 3(-4-0) = 0.

For the second line segment, we have ∫(-4dy -3dx) = ∫(-4dy) - ∫(3dx). Evaluating these integrals gives -4(0-3) - 3(-8-(-4)) = -4.