作者rod24574575 (天然呆)
看板NTU-Exam
标题[试题] 99下 薛克民 微积分甲下 第五次小考
时间Mon Jun 27 19:47:07 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）︰100/5/23
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 :
Write down all the details or you may not get the full grades.
There could be some problems on the back of the paper.
A. Let R be the region cut out by (x^2) + (y^2) ≦ 2, (x^2) + (z^2) ≦ 1 and
x ≧ 0, y ≧ 0, z ≧ 0.
Evaluate the integral ∫ xyz dxdydz
R
-[2(x^2) + (2√2)xy + 3(y^2)]
B. Evaluate the integral ∫∫ e dxdy
R^2
C. (a) Find the work done by the gravitational field
mMG
F(x) = -
──── * x , x € R^3 (这里的 x 皆是向量)
|x|^3
in moving particle with mass m alone the curve (cos(t), -t, t)
from (1, 0, 0) to (0, -π/2, π/2)
2xy dx + (x^2) dy
(b) Evaluate ∫ ──────────
C 1 + (x^4)(y^2)
C is the curve x = log t, y = 2(t^2), 1 ≦ t ≦ √2
2
D. Evaluate the integral ∫ sin(2x + 2y + z) dxdydz
R
R = {(x,y,z)│(x^2) + (y^2) + (z^2) ≦ 16, 0 ≦ 2x + 2y + z ≦ 3π
2x + 2y + z
Hint: Let u = ───────and use polar coordinate on every plane
3
2x + 2y + z = k for all k is a constant.
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