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Asked Dec 1, 2019
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Use double integration to find the volume of the solid

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The wedge cut from the cylinder 4x2+y2=9 by the plane z=0 and z=y+3

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12:33 PM
Drill04-Do...Integrals
Page 5 of 7
MATH 201 - Calculus 3
Practice Drill 4
6. Use double integration to find the volume of each solid
(a) The solid bounded by the cylinder x2 +y2 = 9 and the plane z = 0 and z = 3 - x
(b) The wedge cut from the cylinder 4x2 +y2 = 9 by the plane z = 0 and z = y +3
(c) The solid in the first octant bounded above by x222 = 4 and x2-+y2 = 4
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74 12:33 PM Drill04-Do...Integrals Page 5 of 7 MATH 201 - Calculus 3 Practice Drill 4 6. Use double integration to find the volume of each solid (a) The solid bounded by the cylinder x2 +y2 = 9 and the plane z = 0 and z = 3 - x (b) The wedge cut from the cylinder 4x2 +y2 = 9 by the plane z = 0 and z = y +3 (c) The solid in the first octant bounded above by x222 = 4 and x2-+y2 = 4 6/7

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Expert Answer

Step 1
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4x2y29 9-y 4 V =[ ry+3 dzdxcy L - +3 °dxdy 4 t

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Step 2
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9-y2 (y+3)cdy 4 =L(v+3)(= -L+3)(-yv (9-y py3-y t

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