37.[22, 2] by [21, 2]The curves intersect at (61, 1).(a)A cross section has radius r512x2and area A(x)5pr25p(12x2)25p(122x21x4). The volume is E121p(122x21x4) dx5p3x2}23}x31}15}x545}1165p}.(b)Use cylindrical shells: a shell has radius 22yandheight 2ˇyw. The volume is E102p(22y)(2ˇyw) dy54pE10(2ˇyw2y3/2) dy54p3}43}y3/22}25}y5/245}5165p}.(c)Use cylindrical shells: a shell has radius y11 andheight 2ˇyw. The volume is E102p(y11)(2ˇyw) dy54pE10(y3/21ˇyw) dy54p3}25}y5/21}23}y3/245}6145p}.38. (a)A cross section has radius r5h112}bx}2and area A(x)5pr25ph2112}bx}22. The volume is Eb0ph2112}bx}22dx5ph232}b3}112}bx}2345}p3}bh2.(b)Use cylindrical shells: a shell has radius xand heighth112}bx}2. The volume is Eb02p(x)h112}bx}2dx52phEb01x2}xb2}2dx52ph3}12}x22}3xb3}45}p3}b2h.
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