Answer:
the integral I=81
Step-by-step explanation:
for the integral I
[tex]I=\int\limits^{}_{}\int\limits^{}_{}\int\limits^{}_{T} {x^{2} } \, dxdydz[/tex]
where T is the solid tetrahedron , then
[tex]I=\int\limits^{3}_{0}\int\limits^{3}_{0}\int\limits^{3}_{0} {x^{2} } \, dxdydz = \int\limits^{3}_{0}dz\int\limits^{3}_{0}dy\int\limits^{3}_{0} {x^{2} } \, dx = (3-0)*(3-0)*1/3*(3^{3}-0^{3}) = 3^{4} = 81[/tex]
the integral is equal to 81
