EXAMPLE 1Finding a VolumeFind the volume of the region D enclosed by the surfaces z = x? + 3y? and z =8 - x?MtLeaves atz = 8 - x - y?z = 8 - x -y?The curve of intersectionD(-2,0, 4)(2, 0, 4)Enters atz = x + 3y?Enters atT-2,0.0)y=-V(4 -x)/2+2y? = 4(2,0, 0)Leaves aty = V(4 -218

Answered: Image /qna-images/answer/8fa95129-7c84-42c3-b185-bbb33f431747.jpg

EXAMPLE 1 Finding a Volume Find the volume of the region D enclosed by the surfaces z = x? + 3y? and z 8 - x? - y?. Leaves at z = 8-x- y z= 8 - x -y? The curve of intersection D (-2,0,4) (2, 0, 4) + 3y Enters at z =x + 3y? 2,0.0) Enters at y= -V(4-x/2 (x, y) +2y = 4 (2,0, 0) Leaves at y= V(4 - x)/2 18

EXAMPLE 1 Finding a Volume Find the volume of the region D enclosed by the surfaces z = x? + 3y? and z 8 - x? - y?. Leaves at z = 8-x- y z= 8 - x -y? The curve of intersection D (-2,0,4) (2, 0, 4) + 3y Enters at z =x + 3y? 2,0.0) Enters at y= -V(4-x/2 (x, y) +2y = 4 (2,0, 0) Leaves at y= V(4 - x)/2 18

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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