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,...
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...
The region R in the first quadrant bounded by the curve y = x2 + 1 and the line y = 3x + 1 is revolved about the line y = 1. SKETCH the solid of revolution and find its VOLUME by i) The Washer Method ii) The Shell Method
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the solid obtained by revolving the region R about the r-axis If you slice the region R into thin horizontal slices, i.e., parallel to the r-axis, in setting up the Riemann sum, then which method will come into play? A. Disc method B. Washer method C. Either disc or a washer method depending on the shape...
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...
5 pts) Consider the region bounded by the curves y 9, y and r 1 r-+64 If this region is revolved around the x - axis, the volume of the resulting solid can be computed in (at least) two different ways using integrals. (Sketching the graph of the situation m (a) First of all it can be computed as a single integral h(r)dr where o and This method is commonly called the method of Enter 'DW' for Disks/Washers or 'CS...
#35 and 43 35-38. Shell and washer methods Let R be the region bounded by the following curves. Use both the shell method and the washer method to find the volume of the solid generated when R is revolved about the indicated axis.. 35. y = x, y = x1/3, in the first quadrant; about the x-axis y = - y = 1 - about the x-axis x + 1) 37. y = (x - 2)3 – 2, x =...
Problem 5: 6 pts) The base of a solid is the region in the ry-plane bounded by 2+2 32 and y and is shown below. Cross-sections through the solid taken parallel to the y-axis are semicircles. Set up, but do not evaluate, an integral or sum of integrals that would give volume of the solid. 32 Problem 5: 6 pts) The base of a solid is the region in the ry-plane bounded by 2+2 32 and y and is shown...
3. Consider the region R, bounded by the function f(x) and the x and y values shown. Write down an integral for the volume of the solid obtained by revolving R about the given line. Indicate what method you use in each case. 3 f(x) 2 R (Disk, Washer, or Shell) 1 You do not need to simplify but be sure to include the proper bounds on your integrals. a) The y-axis. Method: b) The line y =1. Method: c)...
IMath 1021sec 6.41Page 8bu Example. Let R be the region bounded by the graph of y sin x2, the x-axis, and the vertical line x Tt/2. Use Shell sin x method to find the volume of the solid of revolution obtained by revolving R about Height 2 = sin x the y-axis, 0 VT/2 Interval of integration IMath 1021sec 6.41Page 8bu Example. Let R be the region bounded by the graph of y sin x2, the x-axis, and the vertical...
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