Question

Calculate the line integral of F = -5i - 3j along the line segment from (-2,5) to (-1,5).

a) -8
b) -10
c) -13
d) -15

Answer 1

To calculate the line integral of the vector field F = -5i - 3j along the line segment from (-2,5) to (-1,5), find the dot product of the vector field and the tangent vector to the line segment. The line integral is -5.

Step-by-step explanation:

To calculate the line integral of the vector field F = -5i - 3j along the line segment from (-2,5) to (-1,5), we need to find the dot product of the vector field and the tangent vector to the line segment. The tangent vector to the line segment is (1,0) since the line only moves horizontally. So, the line integral becomes:

∫C F · dr = ∫C (-5i - 3j) · (dt) = ∫C (-5) dt = -5∫C dt

The length of the line segment from (-2,5) to (-1,5) is 1 unit. So the line integral becomes: -5(1) = -5.

Therefore, the correct answer is (d) -15.