課程名稱︰微積分甲上
課程性質︰必修
課程教師︰周青松
開課學院：管理學院、生農學院、理學院
開課系所︰工管系科管組、生機系、生工系、地質系
考試日期（年月日）︰2010/12/10
考試時限（分鐘）：50分鐘
是否需發放獎勵金：是
試題 :
I.(25%)Evaluate the following integral.
3π/2 ｜2sinx ,0<= x <=π/2
∫ f(x)dx , where f(x)=｜
0 ｜2+cosx ,π/2< x <=3π/2
II.(25%)Given f''(x)=sinx , f'(0)=-2 and f(0)=1. Find f.
III.(25%)The region between y=cosx and the x-axis for x屬於[0,π/2] is divided
into two subregions of equal area by a line x=c. Find c.
IV.(25%)Sketch the region Ω bounded by the curve y=x^2 and y=2-|x| and use
the shell method to find the volume of the solid generated by revolving
Ω about the x-axis.
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