10. Neatly sketch the region enclosed by the graph of y = Vx, the x-axis, and...
The region enclosed by y = Vx and y = 5x is rotated around the x-axis. Choose the integral that can be used to find the volume of the solid of revolution. & S (x - 12 ) dx = [" (432 – y") dy
8. Use the shell method to set up and evaluate the integral y- 3x that gives the volume of the solid generated by revolving the plane region about the y-axis. a. 192R b. 384x C. 192x d. 384x e. 96x 7 9. Set up and evaluate the definite integral for the area of the surface formed by revolving graph of y-9-2 about the y-axis. Round your answer to three decimal places. 8. Use the shell method to set up and...
Please solve #13 and #17. In Exercises 13-16, use the shell method to set up and evaluate the integral that gives the volume of the solid generated hy revolving the plane region about the x-axis. 14.,-2-х 13.) у х 12 -2十 In Exercises 17-20, use the shell method to find the volume of the solid generated by revolving the plane region about the indicated line. x2, y 4x x2, about the linex-4 y In Exercises 13-16, use the shell method...
Please help with 1-10 and please show all work thanks. Show all of your work neatly, and express solutions as exact answers unless otherwise requested. No credit will be given to solutions that have no work shown! BOX or CIRCLE your final answer. 1. Sketch a graph and shade the area of the region bounded by the following equations. Set up an integral that would give this area. 2x + y2 = 6 and y=x+1 2. Sketch a graph and...
Find the volume generated by revolving about the x-axis, the region enclosed by y=x^2+1 and 3x−2y=−4 Be sure to draw the region in the x-y plane, label the axis of revolution, state your method (disc or shell), draw a rectangle to be rotated, label the thickness (dx or dy), state the integral, and sketch the resulting 3D shape. State the volume exactly. show all work please.
2/6 2" (10%) (a) Sketch the graphs of the two functions y=z(4-z) and y=z and mark the finite region (R) enclosed between them. (Identify (R) carefully!) (b) Let W be the volume of the solid of revolution obtained by revolving the above region (R) around the y-axis. (i) Use the shell method to write down the integral for W. (No need to evaluate the integral.) (ii) Repeat part(i) by using the disk method. 2/6 2" (10%) (a) Sketch the graphs...
2. [8 pts] Consider the region R enclosed by the graphs of functions f(x) = 2 – 22 – 2x + 3 and g(x) = -2 +3 + 5 with points of intersection (-1,3) and (2,3), as shown in the figure. (a) Set up but do not evaluate the integral that repre- sents the volume of the solid resulting from revolving the region R about the vertical line r = 3. NA (b) Set up but do not evaluate 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...
Q2 Figure Q2 illustrates a graph that contains two parallel straight lines, with a shaded region bounded by both lines and both axes. y Line A Line B Figure Q2 (a) Find the equation of Line A and Line B respectively. (2 marks) (b) (c) Compute the area of the shaded region. (3 marks) The shaded region is revolved around y - axis. (i) Compute the volume of solid generated by revolving the bounded region between Line A and both...
Consider the solid revolving about the x-axis the region bounded by the curve y= VX, the line y = 8 -2x, and the line y = 0. a Express the volume of the described solid in terms of integrals. Name the method you are using. b. Find the volume of the solid by evaluating the expression found in part (a).