Question

8. Use the shell method to find the volumes of the solids generated by revolving the region bounded by y8 d x 0 about the following lines: yx b) the line = 3 a) the y-axis a) (continued on the next page...) 8(continued) Use the shell method to find the volumes of the solids generated by revolving the region bounded by y x', y=8, and x=0 about the following lines: c) the line x-2 d) the x-axis d) c) e) the line y= 8 f the line y -1 e) f)

Answer 1

N~) Απτh dx where shell radiuo h: shell haight 2 , ha verhical heigh Here, 2 X XO J4υπκ- 2πεί) έκ - 8n (-Απαλλ 16 2 2 7327 7 x 32 32- 647 =160 m-61m 9677 Sp

g-x3 wnere, Shell vadiuo h: shell haight 2 3-MNW 3-x ha verhical heigh = 8-3 Here, J V: 2 (3-x) (8-x3) dx dx S4-3x3- 9x +x uca)-n2-4x2+ R48-12 16 + 26477

whre Shell radius h: shell haight Here, X8-2 Y24 ha vertical heigh 8-x3. V: & 16-2x3+8x -xdx -dn T16-2x3+ 8x-x' + et )nl up- an 32-8 t IG 37 sdn 168 336 4-w

VaTh dy x3 yec atius buill be wewpicaf now. 43-y3 43 /3 8 ny.ys dyeT.y 3 n (a) n 12xT = 8-9 he ys VJan (8-y)ydy 1/3 2 16T

/3 162 X X 12 Tx 2 ㅠ [192 76 x2 24 768 9367