24. y = x, y = 2x/(1 + x)); about x = -1 Question for 24^ : (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. (b) Use your calculator to evaluate the integral correct to five decimal places. 29-32 - Each integral represents the volume of a solid. Describe the solid. 32. 2TT(T - x)(cos x - sin x) dx42. Suppose you make napkin rings by drilling holes with dif- ferent diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height h, as shown in the gure. (a) Guess which ring has more wood in it. (b) Check your guess: Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius 1" through the center of a sphere of radius R and express the answer in terms of h. 3-7 . Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. 6. y = 4x - x, y =x 9-14 - Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. 14. x + y = 3, x =4 - (y - 1) 15-20 - Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. 18. y = x2, y = 2 - x2; about x = 1