Find the mass of an object which is in the form of a cuboid#[0,1]×[2,4]×[1,3]#.The density at any point #(x,y,z)# on the cuboid is given by #delta(x,y,z)=x^2+y^2+z^2# ?

1 Answer
Cesareo R.
Feb 18, 2018

#56#

Explanation:

The mass is obtained by calculating

#int_1^3(int_2^4(int_0^1delta(x,y,z)dx) dy) dz =#
#=int_1^3(int_2^4(int_0^1(x^2+y^2+z^2)dx) dy) dz =#
#=int_1^3(int_2^4(1/3x^3+y^2 x+z^2 x)_(x=0)^(x=1)dy)dz = #
#=int_1^3(int_2^4(1/3+y^2 +z^2)dy)dz = #
#=int_1^3(1/3y+1/3y^3 +z^2 y)_(y=2)^(y=4)dz = #
#=int_1^3((4-2)/3+1/3(4^3-2^3) +(4-2)z^2)dz = 56#

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