作者assignment (凝願)
看板NTUBA00study
標題[轉錄][試題] 94上 黃漢水 微積分乙 期末考
時間Fri Nov 23 23:29:42 2007
※ [本文轉錄自 NTU-Exam 看板]
作者: aphlik (被踹飛的兔子) 看板: NTU-Exam
標題: [試題] 94上 黃漢水 微積分乙 期末考
時間: Thu Jan 12 17:16:59 2006
課程名稱︰微積分乙上
課程性質︰共同必修
課程教師︰黃漢水
開課系所︰經濟、地理等系及管院各系
考試時間︰2006.01.12
試題 :
1.Find the following integrals:(30%)
e ln(x^2)
(1)∫ --------- dx
1 x
1 2
(2)∫ ------------- dx
0 e^(-x) +1
1
(3)∫ 5^(3x) dx
0
1
(4)∫ e^(x) cosx dx
0
2. Let D be the region bounded by the curve y= 2/(x^3) and the lines
x=1,x=2,y=0.(30%)
(1)Find the area of the region D.
(2)Find the centroid of D.
(3)Find the volume of the solid generated by revoloving the region D
about the line x=2.
(4)Find the value c such that the line x=c divides the region D into
two regions of equal area.
2 (x^(3/2))
3. Find the length of the curve y= ------------ +3 . 0≦x≦9. (15%)
3
3x t^2 +1
4. Let h(x) = ∫ ------------- dt for any x>1 . (15%)
x+1 (t^2 +2)^2
Find h'(x), h'(2).
5. (1)Find a real number k such that
________ ______ ______
∫2 /x^2 +9 dx = x /x^2 +9 + kln│x + /x^2 +9│ +c. (5%)
v v v
4 ______
(2)Find the integral ∫ /x^2 +9 dx. (5%)
3 v
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