Determine the volume of the sold in the 1st octant bounded by x+y+2z=4

Rui Baldwin 2020-10-20 Answered
Determine the volume of the sold in the 1st octant bounded by x+y+2z=4
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Anonym
Answered 2020-10-21 Author has 108 answers
Step 1
The given equation is:
x+y+2z=4
The above equation is solved as:
2z=4xy
z=2x2y2
Thus,zvaries0z2x2y2
In XY plane , the equation is:
x+y=4
Thus, y varies in 0y4x
and x varies in 0x4
Step 2
The volume is given as:
Volume=0404x02x2y2dzdydx
=0404x[z]02x2y2dydx
=0404x(2x2y2)dydx
=04[2yxy2y24]04xdx
=04[2(4x)x(4x)2(4x)24]dx
=04[82x2x+x22(168x+x2)4]dx
=04[82x2x+x224+2xx24]dx
=04[42x+x24]dx
=[4x2x22+x312]04
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