Ecuaciones de bernully

21. z=y2
0≤x≤4,
0≤y≤2
0402y2 dydx => 04y24 20 dx => 0414 (22) dx => 04dx => x 40
V = 4

22)
z =6-2y
0≤x≤4,
0≤y≤2

V = 02046-2ydxdy=> v = 026 04dx-2y04dx dy
V = 026x40- 2y x 40 dy => V 20 24-2y 4dy
V = 24 20 dy-8 20y dy => V = 24 y 20 - 8y22 20 => 24 (2)- 4 (4)
V = 48 – 16 => V = 32

23 )
z= 4 - x – y
y =x
y = 2
V = 022x(4 - x – y)dydx=>
V = 2 0 [4 x 2 dy – x x 2 dy - x 2 y dy ] dx => V = 2 0 [4x – 8 x2+ 2x - x22+ 2]dx
V = 2 0 [-3x 22 + 6x – 4] dx
V -2 0 3x 22dx + 6 2 0 x dx-4 2 0 dxV = - x 2220+ 3x220- 4 x20 => v -12 + 12 – 8 => v = 72

24. z=4
y= x
x= 2
V= 020x4dydx=> V 20 4xdx => V = 4x2220
V = 2x2 => V = 2(4) => V = 8

25. 2x+3y+4z=12
x= 12-3y-4z2
Z = 3
0≤z≤3

3y = 12 >> y = 4 => 0 ≤y ≤4
V = 123040(12 – 3y -4z) dy dz => V = 1230( 12 40dy – 3 40y dy – 4z 40dy ) dz
V= 1230[12 4- 32 42 – 4z (4)] dz=> v 12 30 48-24-16Zdz
V = = 1230 24-16 Zdz => V= 12 ( 24z 30- 8z2 30) => V = 12 (24 3- 8 9)
V = 48 – 36 => V = 12

26 )
X+ y+ z = 2
z=2-x-y
X = 2 0≤x≤2y= -x+2 0≤y ≤2-x

V = 202-x0(2-x-y) dy dx
V = 20(2 2-x0 dy-x 2-x0dy - 2-x0 y dy ) dx
V = 20(2y 2-x0 - xy 2-x0 – 12y2 2-x0) dx
V = 20[4 – 2x -2x + x2 – 12(4- 4x + x2) ] dx
V =20(4 – 4x + x2 – 2 + 2x - x22 )dx => V = 20( 2 – 2X +x22) dx
V = 2 20dx-2 20x dx+ 1220 x2 dx = > V = 2x 20 - x2 20+ 116 x320
V = 4 – 4 + 86 = > V = 43

27)
Y = x ,y =1, z=1-xy
0≤y ≤1
0 ≤x ≤y
V = 10y 0 1-xydxdy => V= 10 [y0dx – y y0 x dx ] dy
V = 10( y - y32) dy => V = 10ydy - 1210y3 dy => V = 12 y210- 18y4 10
V = 12- 18=> V = 38
28)
V = 20y0(4 – y2)dx dy = 20y0 (4 - y2 )dx dy
V = 20[4 y0- y2xy0] dy => V= 20 [4y – y3] dy
V = 204 y dy - 20 y3 dy => V 2y220- y442 0 => V = 2(4) - 14 (24)
V =...