課程名稱︰微積分乙上
課程性質︰管院必修
課程教師︰陳逸昆
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/1/2
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(11%) Find the area of the region enclosed by the curves y=x^2-3x+1 and
y=x-2.
2.(6%) a. Evaluate
d x √(1+t^2)
---∫ --------- dt.
dx 1 t
(6%) b. Evaluate
d x^2
---∫ arctan(e^t+sin(t^3)) dt.
dx 1
3.(11%) Evaluate
x^3+1
∫----- dx.
x^3+x
4. Let E be the region on xy-plan bounded by the curves y=lnx , x=2 and y=0.
(11%)a. Find the volume of the solid obtained by rotating E about the y-axis.
(11%)b. Find the volume of the solid obtained by rotation E about the x-axis.
5.(11%) Find the arc length of the parabola y=0.5x^2 from (0,0) to (2,2).
6.(11%) Find the area lies under the graph y=x^2√(4-x^2) between x=0 and x=2
7.(11%) Determinate whether the improper integral
∞ 1
∫ -------- dx
2014 x(lnx)^2
is convergent or divergent. If it is convergent, evaluate the value.
8. A probability density funciton is given as follows:
0 ,if x＜0
f(x)={
e^-x,if x≧0
(5%) a. Find the mean of f.
(6%) b. Find the standard deviation of f.
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