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...
show works please Q9 10 Points Let R be the region bounded by the curve y = x2 + 1 and the lines x = 0, x = 1, and y = 1. (a) Set up, but do not evaluate, the volume of the solid obtained by rotating R about the x-axis. Show your work. (b) Set up, but do not evaluate, the volume of the solid obtained by rotating R about the line 2 1. Show your work. =
need it asap please 18) 8. The region is bounded by y = 2 - r- and y = r. (a) (2 marks) Sketch the region. (b) (6 marks) Find the area of the region. (c) (5 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 r = -3. (d) (5 marks) Use the disk or washer method to...
calculate volume The region R is bounded by the curves y = 22 +1 and y = 3x - 1. Set up an integral blume of the solid obtained by rotating R about the line x = 4. Then calculate the
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...
1.The region R is the region bounded by the functions y=x-3 and x=1+y^2. find the volume of the solid obtained by rotating the region R about the y axis. Please include a graph. 2.Find the volume of the solid obtained by rotating the region bounded by the graphs of y=x and y=sqrt(x) about the line x=2. Please include a graph
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. y= e- y0, x= -5, x-5 (a) About the x-axis (b) About y-1 Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate...
Problem 1 part II and Problem 2 part I and II Problem 1: (Short Answer) 6 pts] The region R is bounded by y 0, 0, 2, and y- 2 4 1, 3 pts] If R is revolved about the line x = 5. If an integral or sunn of integrals with respect to z is used to calculate the volume, explain whether the washer or shell method should be used II. 3 pts) Suppose that R is the base...
Region R is bounded by lines y=√x and y=x. A solid is obtained by rotating region R about line x=-1. Express the volume of this solid in the form if an integral.
Consider the region bounded by y = (1 - 2)2 and y = 4 - r. For each of the following, set up (but do not compute) integrals that determine the volume of the solid obtained by rotating the region around the specified axis: (a) The y-axis. (b) The line r = 5. (c) The line y = -1.