10. The region bounded by y = x², y = 3x, is revolved about the x-axis....
8. The region bounded by x = 3/7, x = 0, y = 8 is revolved about the y-axis. a) Sketch the region b) Sketch the solid and a representative shell. c) Set-up the integral to find the volume using cylindrical shells. DO NOT SOLVE!!!
9. The region bounded by y = x2, y = 3x, is revolved about the x-axis. a) Sketch the region b) Sketch the solid and a representative disk/washer. c) Set-up the integral to find the volume using disks/washers. DO NOT SOLVE!!!
7. The region bounded by x = 3/7, x = 0, y = 8 is revolved about the y-axis. a) Sketch the region b) Sketch the solid and a representative disk/washer. c) Set-up the integral to find the volume using disks/washers. DO NOT SOLVE!!!
The region Bounded by the curves y=x2 is revolved about the x-axis. Give an integral for the volume of the solid that is generated. The region bounded by the curves y = 3x and y = x' is revolved about the x-axis. Give an integral for the volume of the solid that is generated. va | ndx (Type an exact answer using a as needed.)
1. Consider the region bounded by the y-axis and the functions y and y-8 Set up (but do not evaluate) integrals to find (a) The area of this region. (b) The volume of the solid generated by rotating this region about the y ad sn axis using shells. (c) The volume of the solid generated by rotating this region about the vertical line r5 using washers 2. Set up (but do not evaluate) an integral to ind the work done...
all answer Sample Test 4 1575 Calculus II 1. The region bounded by the parabola y-4x-x and the x -axis is revolved about thex- axis. Find the volume of the solid. Write answer in term of π. Find the area enclosed by the curves: 2. y=2x2-4x-12 y=x2-6x+12 and 3. Find the volume of the solid obtained by rotating the region bounded by the graphs of a. y-x-9, y 0 about the x-axis. -1 about the x-axis. b. y 16-r, y-3x+...
3. (a) If the region sketched in (1) above is revolved about the line y -0 (x-axis), sketch and label the typical rectangle(s) needed to use the shell method to find the volume of the resulting solid. (b) Use the shell method to find the volume of the resulting solid 2 pts [9 pts] 4. (a) If the region sketched in (1) above is revolved about the line x-O。-axis), sketch and label the typical rectangle(s) needed to use the disk/washer...
both parts please Consider the region in the first quadrant bounded by the curves y = 3x, y = 3 - (x - 1)2, and y = 2. (a) Sketch the region. Note all points of intersection. (You may use GeoGebra if necessary, but you can probably do it faster by hand.) (b) Using either the washer or shell method, set up (but do not solve) an integral that computes the volume obtained when the region is revolved about the...
6. (a) (1 marks) Sketch the region bounded by the curves y = sin x, y = x+1, x = 0 and x = - 27. (b) (3 marks) Use the method of cylindrical shells to set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region about the line x = 27. (c) (3 marks) Use the method of washers to set up, but do not evaluate, an integral for the...
Problem 3 6 pts] The region R bounded by y V, y 0, and 4 is revolved about the line y3 Calculate the volume of the solid using the washer method and simplify your final answer. -3 Problem 4: 8 pts] The region R is boud by y2 and y 8- 2 I. Set up, but do not evaluate, an integral or sum of integrals that would give the volume of the solid of revolution formed when R is revolved...