# 12 use cylindrical shells to compute the volume of

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12.Use cylindrical shells to compute the volume of the region bounded by2xyandx= 4revolved abouty= 2,.
y = 2(2*)**(2( )( )babaVradiusheightthicknessVy fy dy220223022234432004322(2)(4)2(824)42242828234432(2)2(2)4(2)(16)2(8)4(4)28(2)216432432Vyydyyyydyyyyyyyyy1616361624816021223312122023403V22.Use the best method available to find the volume of the region bounded by22,(0)yxyx x and they-axis revolved about (a) thex-axis, (b) they-axis, (c)–1, and (d)y= –1.x=
(a)Revolved about the x-axis211222242001153240053244545453(1)5(1)154(1)4535352560401515151583bo iaVrdxxxdxxxxdxxxxxdxx(b) Revolved about the y-axis143243202(1)(1)2(1)224324321123412127222432121212121256xxxVWA 1, p. 17y = xy = 2-x2y = 0y = -1x = -1x = 0

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