作者fong1014 ()
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标题[试题] 97上 黄汉水 微积分甲 期末考
时间Fri Jan 16 11:46:31 2009
课程名称︰微积分甲(上)
课程性质︰大一共同必修
课程教师︰黄汉水
开课学院:生农学院、理学院、管院
开课系所︰生机、生工、工管(科管组)、地质等系
考试日期(年月日)︰2009/1/6
考试时限(分钟):100分钟
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
一.Find the following integrals: (30%)
π
(1) ∫ tsintdt
0
2 7x^3+8x^2+5x+7
(2) ∫ -------------------- dx
1 x^2+x^4
ln3
(3) ∫ tanht dt
0
3x
二.Let H(x)=∫ (t^4+1)^(1/2)dt. (15%)
x+2
Find the function H'(x) and the value H'(1),H'(2).
1
三.Let In(t)=∫(t^n)(e^-t)dt, Jn=∫(t^n)(e^-t)dt (20%)
0
(1)Find the relation between In(t), I(n-1)(t).
(2)Find the relation between Jn ,J(n-1)
(3)Find the value J1,J2,J3,J4
四.Let D be the region bounded by the curves y=lnx, y=0,x=e.
(1)Find the area of D. (5%)
(2)Find the volume of solid generated by revolving the region D
about the line y=0. (10%)
(3)Find the centroid of the region D. (10%)
五.Let D={ (x,y,z)│x^ + y^2 + z ≦ 2 , z ≧ 0 }
Find a plane z=c which divides the region D into two parts of equal
volume.(10%)
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