Question

1. Use the method of cylindrical shells to find the volume of the following solids rotation (i) Spin the region bound by y -Vx,y 0, x-1 around the y-axis; (ii) Twist the area bound by x -1+(y-2)2 andx- 2 about the x-axis; (iii) Rotate the region between y - x2 and y -6x-2x2 around the y-axis; (iv) Twirl the space between y V and x 2y about the line x 5 2. Use both methods discussed in class to compute the volume of the solid obtained by spinning the region bound by the y-tan (x), x 1,4, and y-0 around the y-axis. 3. Find the length of the following curve segments: (i) y = x-log(x) between l s s 4; (i) y between 1 ss2; (i) y log(sec(x) between 0sxsT/4; (iv) y= between-is x l. 3 4x 4. Find the length of the curve defined by 2/3+y23. In setting up you integral, it may be helpful to use the symmetry of this curve.

Answer 1

0. 471 木1 2.2956 2/3