1.

Let S denote the solid obtained by rotating the region shown in the figure about the y-axis. y y = a sin(bx?) VT/b X Which of the integrals below correctly expresses the volume of S'? O / T/b A. 2ra sin (bac? ) dac O TT / b B 27xa sin(bx2 ) dac 0 O a C . arcsin(y/a ) dy 0 b O D. T a sin(bac2) ) dac O E. None of the aboveLet 5 denote the solid obtained by rotating the region shown in the figure about the line a: = 1. Which of the integrals below correctly expresses the volume of S? O w/b A. / 27r(:r: l 1)a sin(bzc2)d:1: 0 0 8.] 7r (_a.rcsn;(y/a) + 1) dy 0 O 7r/b 2 C. f 7r ((1 sin(b:1:2) + 1) d3: 0 O 17/!) D. / 21 (a: sin(b;1:2) + 1) d2: 0 O E. None of the above Let 5 denote the solid obtained by rotating the region shown in the figure along a line a: : c (where this line is to the right of the region; i.e., c > 1/ 7T/b). Which of the integrals below correctly expresses the volume of S? 0 fr/b A. / 27r(c $)asin(b$2)d$ 0 0 17/5 B. [J 271' (a Sin(bm2) (3) d3: 0C (3/03\" (axGamma) +6) dy 0D. /m 27r($ (2)0, sin(bm2)da: 0 O E. None of the above Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the graphs ofy : 43: 332, y : :1: about the y-axis