作者KenYang0531 (羊咩咩)
看板NTU-Exam
标题[试题] 98下 陈宏 微积分甲下 第九次小考
时间Sat Jul 10 18:50:43 2010
课程名称︰微积分甲下
课程性质︰系内必带
课程教师︰陈宏
开课学院：工学院
开课系所︰土木工程学系
考试日期（年月日）︰2010/5/25
考试时限（分钟）：20min
是否需发放奖励金：是，谢谢
（如未明确表示，则不予发放）
试题 :
·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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