Consider a force ⃗F=-x̂i+ŷj. The work done by this force in moving a particle from point A(1,0) to B(0,1) along the line segment is (all quantities are in SI units)

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(3) 1. W=∫⃗F· d⃗r=∫(-x dx+y dy). Along the segment x runs from 1 to 0 and y from 0 to 1; each term integrates on its own variable. ∫₁⁰(-x) dx=[-(x²)/2]₁⁰=1/2 and ∫₀¹y dy=1/2. W=1/2+1/2=1 J.

Consider a force ⃗F=-x̂i+ŷj. The work done by this force in moving a particle from point A(1,0) to B(0,1) along the line segment is (all quantities are in SI units)

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