Evaluate the integral:int int int_E(xy+z^2)dV, where E={(x,y,z)|0<=x<=2,0<=y<=1,0<=z<3}

CoormaBak9 2021-02-21 Answered

Evaluate the integral:
E(xy+z2)dV,
where E={(x,y,z)0x2,0y1,0z<3}

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Expert Answer

oppturf
Answered 2021-02-22 Author has 94 answers

Here we have to evalute the integral (xy+z2)dxdydz over the regin bounded by 0x2,0y1,0z<3. Then
(xy+z2)dxdydz=x=02y=01z=03(xy+z2)dxdydz
=x=02y=01(xyz+(z33)z=03dxdy
=x=02y=01(3xy+9)dxdy
=x=02(3xy22+9y)+(y=0)1dx
=x=02(3x2+9)dx
=(3x24+9x)x=02
=(3+18)
=21

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