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四、若在一只培養皿中加入碘化鉀溶液以及數滴無色酚酞溶液後，再以兩支鉛
筆芯與一個 6-V 直流電池對其進行電解，則在培養皿右上方的筆芯周圍會
顯現粉紅色，而在左下方的筆芯周圍，會顯現黃褐色，如下圖所示。根據
所述，回答下列問題：
10. (10 Points) Evallate the line interal 
along
the curve C : r(t) = (t2+1)i+ (t2 - 1)j, 0 ≤ t ≤ 2. Hint you may find a
potential function f of the vector field F(x,y) =
find f so that F = ∇f.
9.(10 Poins) Evaluate the triple integral 
, where E is the solid
region in 
bounded by the surface z = 1 and z = x2+y2.
8. (10 Points) Evaluate the double integral 
, sin(x+y)dA where D is the regsion
bounded by x+y= π, x+y = 0 and x -y =π and x-y=0.
