课程名称︰微积分甲上
课程性质︰大一必修
课程教师︰容志辉
开课学院：工学院
开课系所︰电机系、材料系
考试日期（年月日）︰2014/12/15
考试时限（分钟）：50分钟
试题 :
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103-1 Calculus class-2 3rd test
1. (a) (10%)
3θ 2
∫ e sin 5θ dθ =
(b) (10%)
t 1
∫ ────────── d x =
0 2 2 ( 3/2 )
( a - x )
(c) (25%)
4 3 2i-1 6 3 2j-1
∫ tan x Σ sec x + tan x Σ sec x d x =
i=1 j=1
2. (a) (20%)
3
x
∫ ────── d x =
10
( x-1 )
(b) (20%)
2
x + 2x + 3
∫ ─────── d x =
4
x - 1
(c) (20%)
1
∫ ───────── d x =
2
√( x + 2x + 3 )
3. (25%)
n
√n!
lim ─── =
n→∞ n
4. (20%) Find the volume generated by rotating the region bounded by the given
curves about the specified axis.
6
(a) (10%) y = x , y = 0 , x = 1; about x = 2
4
(b) (10%) x = y + 3 , x = 4; about y = 3
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