課程名稱︰微積分二
課程性質︰數學系大一必修
課程教師︰余正道老師
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2019/6/13
考試時限（分鐘）：180
試題 :
There are 119 points in total
1. [10%] Suppose S, T has area and S is contained in (包含於) T.
(a) Show that the areas satisfy A(S)≦A(T).
(b) Show that T\S has area.
2. [10%] Evaluate the integral ∞
∫ e^(-x^2)dx.
-∞
3. [20%] Let Σ be the surface cut out of the cylinder x^2+z^2=1 by x^2+y^2=1
and z≧0.
(a) Find the surface area of Σ.
(b) Find the volume of the region above the z-plane and below Σ.
4. [10%] Let Σ be the ellipsoid x^2 y^2 z^2