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）︰100/5/23
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 :
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 (這裡的 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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※ 編輯: rod24574575 來自: 218.167.193.80 (06/27 19:48)