课程名称︰微积分甲上
课程性质︰大一必修
课程教师︰朱桦
开课学院：工学院
开课系所︰材料系 电机系
考试日期（年月日）︰2014/12/29
考试时限（分钟）：25分钟
试题 :
CALCULUS QUIZ 6
Instructor: Professor Huah Chu
Quiz date: 29, December, 2014
Quiz time: 25 minutes
Total score: 24 points (Each problem is worth 3 points)
Let C be the curve defined by x^(2/3)+y^(2/3)=1 and R be the region enclosed
by C.
(a) Find the are of R.
(b) Find the length of the curve C.
(c) Find the volume of the solid generated by rotating R about the x-axis.
(d) Find the volume of the solud generated by rotating R about the y-axis.
(e) Find the area of the surface generated by rotating C about the x-axis.
(f) Find the area of the surface generated by rotating C about the y-axis.
(g) Determine the centroid of the curve C in the first quadrant.
(h) Determine the centroid of the region R in the first quadrabt.