Find the limits of integration ly, uy, lx, ux, lz, uz (some of which will involve variables x, y, z) so that ∫uz lz∫uxlx∫uyly? y? x? z represents the volume of the region in the first octant that is bounded by the 3 coordinate planes and the plane x+3y+7z=21.

Question

Mathematics

Luka Oconnell

11 June, 10:02

Find the limits of integration ly, uy, lx, ux, lz, uz (some of which will involve variables x, y, z) so that ∫uz lz∫uxlx∫uyly? y? x? z represents the volume of the region in the first octant that is bounded by the 3 coordinate planes and the plane x+3y+7z=21.

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Answers (1)

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Bridget Trevino · Answer 1

X from 0 to 21

Y from 0 to 7

Z from 0 to 3

Step-by-step explanation:

Since we are being asked by the integration limits in first octant (positive x, positive y and positive z) we need to know where does the plane intersect this axes. For this we have:

for x=0 and y=0

7z=21

z=3

for x=0 and z=0

3y=21

y=7

for z=0 and y=0

x=21

This means that the integration limits are:

X from 0 to 21

Y from 0 to 7

Z from 0 to 3