[轉錄][試題] 94上 張鎮華 微積分乙期末考
※ [本文轉錄自 NTU-Exam 看板]
作者: Roychess (I Love Avril) 看板: NTU-Exam
標題: [試題] 94上 張鎮華 微積分乙期末考
時間: Tue Jan 10 13:18:10 2006
課程名稱︰微積分乙
課程性質︰共同必修
課程教師︰張鎮華
開課系所︰醫學院,公衛學院,生科院...等
考試時間︰2006/01/10 10:20~12:20
試題 :
Examination 3 (Calculus B, first semester)
2006/01/10 (Gerard J. Chang)
＊Each problem weights 10 points.
2a
1.Find a>0 such that ∫ (1-│x│) dx = 0.
-a
d d arctanx
2.Compute ----- arctanx and ------∫ 4 tanu du.
dx dx X
1/3
3.Find the area of the region bounded by y=x ,y=2-x, and the x-axis.
1/2
4.Rotate the area bounded by the curves y=(2x) and y=x about the x-axis,
and compute the volume of the rotation.
5
X 1
5.Find the length of the curve y=---- + ----- from x=1 to x=2.
3
10 6X
1
6.Evaluate ∫(------ + tanx ) dx.
xlnx
1
7.Evaluate ∫ arctanx dx.
0
1/3
X
8.Evaluate ∫e dx.
2
2+X-X
9.Evaluate ∫----------- dx.
2 2
X (X +1)
∞ a
10.Determine all real numbers "a" for which the improper integral ∫ (x+1) dx
0
converges. Justify your answer.
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