2D curve for the given functions :
3D Region generated after rotation about the y-axis :
11. Let R be the region bounded by y=-3x² + 12x - 11 and y=0. Approximate the volume of the solid generated by rotating R about the y-axis.
5. Find the volume of the solid obtained by rotating the region bounded by the curves, y = 2x, x = 0 and y = 10 about the x axis, 5. Find the volume of the solid obtained by rotating the region bounded by the curves, y = 2x, x = 0 and y = 10 about the x axis,
Let R be the region bounded by the following curves. Use the disk method to find the volume of the solid generated by revolving the shaded region shown to the right about the x-axis. y=3-2x, y=0, x=0 Set up the integral that gives the volume of the solid using the disk method. Use increasing limits of integration
5. Define R as the region bounded by the graph of y=2x-r and by the x-axis over the interval [0,2]. Find the volume of the solid of revolution formed by revolving R around the y-axis. Hint: Use Shell Method s
0. Using Let R be a region bounded by y = x?, y = 16 and x = SHELL METHOD, set up an integral to find the volume of the solid generated by revolving R around the line x 8. YOU DON'T NEED TO SOLVE THE INTEGRAL.
Consider a solid whose base is the region bounded by the curves y = (−x^2) + 3 and y = 2x − 5, with cross-sections perpendicular to the y-axis that are squares. a) Sketch the base of this solid. b) Find a Riemann sum which approximates the volume of this solid. c) Write a definite integral that calculates this volume precisely. (Do not need to calculate the integral)
Instructions: Show all your work for FULL credit. Calculators are NOL final answer. Neatness is highly appreciated. 1. A region R, bounded by y 2x, y 6-x, and x-axis, is rotated around the y-axis. Sketch the region R, in the box a) 15 strip/slice you will use to find the volume of the solid of revolution. b) Write the definite integral that gives a X the volume of the solid of revolution. (DO NOT evaluate the integral.) Find the circumference...
4. The region bounded by y = r - 1+1 and x = 2y – 1 is shown in the figure. y= (x-1 +1 x = 2y - 1 (5,3) (1,1) (a) (6 points) Set up but DO NOT EVALUATE the integral(s) that measure(s) the volume of the solid obtained by rotating the region about the x-axis. (b) (6 points) Set up but DO NOT EVALUATE the integral(s) that measure(s) the volume of the solid obtained by rotating the region...
Let R be the region bounded by the y-axis and the graphs and as shown in the figure to the right. The region R is the base of a solid. Find the volume of this solid, assuming that each cross section perpendicular to the x-axis is: a) a square. b) an equilateral triangle. Let R be the region bounded by the y-axis 4. and the graphs y = 1+x2 and y 4-2x 2x y = 4 as shown in the...
Let R be the region bounded by the following curves. Find the volume of the solid generated when Ris revolved about the y-axis. y= (x,y=0, x= 4 Set up the integral that gives the volume of the solid. ody 0 (Type exact answers.) The volume of the solid is cubic units. (Type an exact answer.)