作者rod24574575 (天然呆)
看板NTU-Exam
标题[试题] 99下 薛克民 微积分甲下 第六次小考
时间Tue Jun 28 13:58:37 2011
课程名称︰微积分甲下
课程性质︰必修
课程教师︰薛克民
开课学院：电资学院、工学院、管理学院
开课系所︰电机系、资工系、材料系、资管系
考试日期（年月日）︰100/6/13
考试时限（分钟）：40分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
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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