課程名稱︰微積分甲下 課程性質︰必修 課程教師︰薛克民 開課學院：電資學院、工學院、管理學院 開課系所︰電機系、資工系、材料系、資管系 考試日期（年月日）︰100/6/13 考試時限（分鐘）：40分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. Apply Green's theorem to find the area of the region bounded by the curve parametrized by r(t) = ( cos(t), [sin(t)]^3 ), 0 ≦ t ≦ 2π. (10%) → → → → 2. Find the circulation of the field Ｆ = -(x^2)y ｉ + x(y^2) ｊ + (z^2) ｋ around the curve C in which the circular cylinder (x^2) + (y^2) = 2x meets the cone z = 2√[(x^2) + (y^2)] counterclockwise as viewed above. (10%) 3. Evaluate the integral (10%) ∫∫ y ds S where S is the surface z = x + (y^2), 0 ≦ x ≦ 1, 0 ≦ y ≦ 2 → → → → z ｉ + y ｊ + x ｋ 4. Find the flux of the vector field Ｆ(x,y,z) = ───────────── (x^2 + y^2 + z^2)^(3/2) over the unit sphere (10%) --

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