課程名稱︰微積分甲(上)
課程性質︰系定必修
課程教師︰黃漢水
開課學院：生機、生工、地質、工管
開課系所︰數學系
考試日期（年月日）︰2007/12/24
考試時限（分鐘）：70分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
一 Find the following integrals (40％)
1 _____
(1)∫[(4x-1)/(1+x^2)]dx (2)∫[(2x+4)/√1-x^2]dx
0
二 Let D be the region bounded by the curves
y=x^2 and y=－x^2+4x
(1)Find the area of the region D (15％)
(2)Find the line x=a which divides the region
into two regions of equal area (15％)
三 Let D be the region bounded by the curves
y=x^3，y=0 and x=1
(1)Find the volume of the solid generated by revolving
the region D about the line x=1 (15％)
(2)Find the centroid of the region D (15％)
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