課程名稱︰微積分甲下
課程性質︰系內必帶
課程教師︰陳宏
開課學院：工學院
開課系所︰土木工程學系
考試日期（年月日）︰2010/5/25
考試時限（分鐘）：20min
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
·Make sure to give sufficient reason in each problem or you will NOT get any
credit for your answer.
·There are TWO pages of paper in this quiz.
A.(2 points) Evaluate ∫∫∫(x+y+z)^3 dxdydz.
{x^2+y^2+z^2<=1}
B.(5 points) Evaluate 1/2∮xdy-ydx where Γ is the circle x^2+y^2=1 starting
Γ
form (1,0) to itself counterclockwise.
C.(5 points) Let f(x,y)=tan^(-1)(xy) anf Γ being the curve x^3+y^3=1 from
(0,1) to (1,0). Find ∫▽f·dr.
Γ
-GMm
D.(8 points) Let F=--------x be the gravitational field where x=(x,y,z). Find
|x|^3
the work done by F along the path r=(t,t^2,t^3) from t=1 to t=2.
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