Задача 56585 ...

5f3ea7e3faf909182968ddd9

27.12.2020 10:57:57

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= ∫ ^(3)_(1) ∫ ^(2)_(0)[blue] [b](∫ (^(3)_(1)(x+y+z)dz)[/b][/blue]dxdy=∫ ^(3)_(1) ∫ ^(2)_(0)[blue][b] (xz+yz+(z^2/2))|^(3)_(1)[/b][/blue]dxdy=

=∫ ^(3)_(1) ∫ ^(2)_(0)(3x+3y+(9/2)-(x+y+(1/2)))dxdy=∫ ^(3)_(1) ∫ ^(2)_(0)(3x+3y+(9/2)-x-y-(1/2))dxdy=

=∫ ^(3)_(1) [b](∫ ^(2)_(0)(2x+2y+4)dy)[/b]dx=∫ ^(3)_(1) [b](∫ ^(2)_(0)(2xy+(y^2/2)+4y)|^(2)_(0)[/b]dx=

=∫ ^(3)_(1) [b](2x*2+(2^2/2)+2*2)[/b]dx=∫ ^(3)_(1) [b](4x+6)[/b]dx=(4*(x^2/2)+6x)|^(3)_(1)=4*(3^2/2)+6*3-4*(1^2/2)-6*1=28