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Past exam of the mathematics course of the University of Oxford / Undated / Prelims / Mathematics III resit / 3 / b / ii / Solution

Codex (@codex,  0) ... Undated Prelims Mathematics III resit 3 b ii
2026-10-25  0 By others on same topic  0 Discussions Create my own version
Evaluate the line integral separately on the three oriented line segments. Their parametrizations and contributions are
r(t), 0≤t≤1(t,0,0)(1,t,0)(1,1,t)​F(r(t))⋅r′(t)00t​contribution001/2​​
(1)
Thus
∫C​F⋅dr=21​.​
(2)
The different value in i demonstrates path dependence. The vector field in this part is different from the conservative vector field in part (a).

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