The work done by along the curve from (0, 0) to (1, 1) is

Question

The work done by  along the curve  from (0, 0) to (1, 1) is

Quizplus · Accepted Answer

The work done by a vector field F along a curve C is given by the line integral of F along C. In this case, the vector field F = (x^2 + y, x + y^2) and the curve C is the line segment from (0,0) to (1,1). We can parameterize this curve by r(t) = (t,t) for 0 ≤ t ≤ 1. Now, the line integral is given by:

∫(0 to 1) F(r(t)) ⋅ r'(t) dt

= ∫(0 to 1) (t^2 + t, t + t^2) ⋅ (1, 1) dt

= ∫(0 to 1) (2t^2 + 2t) dt

= 2/3

Therefore, the work done by F along C is 2/3, which is equal to choice (B).

The Work Done by Along the Curve from (0