V y dy y dy 2 5 1 2 5 v y y y 1 25 1 1 2 5 3 10 3 10

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()()Vydyydy2510() |25Vyyy1 = 25((1)(1))25= 310310-0 = 310y0 = 25((0)(0))25= 0 b.) ( )baVA x dx1122200(1)(1)Vydyydy1240( 22)Vyyyy dy3532210(24) |5332Vyyyyy1 35322((1)(1)4(1)(1))5332y= 11301130- 0 1130y0 35322((0)(0)4(0)(0))5332y= 0 26.Let Rbe the region bounded by 2yxand y= 4. Compute the volume of the solid formed by revolving Rabout the given line.(a)y= 4 2( )baVf xdx2222222(4)()Vdxxdx2222(4)Vxdx2242(168)Vxxdx3522(168) |35Vxxxx2 = 2561525615- (25615) = 51215x-2 =25615
WA 1, p. 5 (b)the y-axis 2( )baVf xdx420()Vydy40Vydy240() |2yy4 2((4))2162=162- 0 = 162y0 2((0))2= 0 (c)y= 62( )baVf xdx2222222(6)(2)Vxdxdx22423212Vxx dx= 3522(3212) |35xxxx2 = 1925= 1925- (1925) = 3845x-2 = 1925(d)y= 2 2( )baVf xdx2222222(6)(2)Vdxxdx24223644Vxxxdx53222(3642) |53xxxxx 2 = 58415= 58415- 82415= 140815x-2 = 82415(e)x= 2 2( )baVf xdx442200(2)(2)Vydyydy40(4444)Vyyyy dy3240(16) |3yy4 = 134.0412866 =134.0412866 - 0 = 134.0412866 y0 = 0
WA 1, p. 6 (f) x= 4 2( )baVf xdx442200(4)(4)Vydyydy32240(216) |322yyx4 (16256)3318.3480556=318.3480556- 0 = 318.3480556x0 = 0 32.Suppose that the circle 221xyis revolved about the y-axis. Show that the volume of the resulting solid is 43. 22222111xyxyxy, when x=0, y is -1 and 1 2baVr dy121( 1)Vydy1221(1)Vydy311() |3yyx1 2323- (23) = 43x-1 23 Section 5.3 4.Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by ,,yx yx and 1,xrevolved about 1x. radius= 1-x height= ()xx xx2 ( )( )baVxhdx 102 (1)()Vxxx dx120222Vxxdx32102(22) |32Vxxx1 = 23=23- 0 = 23
WA 1, p. 7

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