R Math166 Practice Exam 1 1. (15) Sketch and nd the area of the region bounded by the curve x = y 2 , x = 6 y and the x-axis.
2. (15) Find the length of the curve x = 3t t3 , y = 3t2 , 0 t 2.
3. (20) A region R is bounded by y = x3 + 1 and y = 0 between x = 0 and x = 2. a. sketch the region b. Set up (but do not evaluate) an integral for the volume of each solid generated by revolving the region about i. the line y = 1. ii. the x line = 4.
4. (15) Find the centroid of the region bounded by the curve y = 2 cos 2x and the x-axis, x . 4 4
5. (15) A right cylindrical tank of radius 4 feet and height 10 feet is initially full of a liquid with density lb/ft3 , nd the work done in pumpin...