By evaluating The Triple Integral. Triple Integral 7x2 DV, Where T Is The Solid Tetrahedron With Verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), And (0, 0, 1) the value calculated is 7/60.
Given:
= ∫∫∫7[tex]x^{2}[/tex] dV
T(x,y,z) : 0≤x≤1; 0≤y≤1-x; 0≤z≤1-x-y]
apply limits and solving we get:
= 7/2([tex](x^{3} /3+x^{5} /5-x^{4}/2)[/tex]
= 7/2(1/3+1/5-1/2)
= 7/2(1*5+1*3/15 - 1/2)
= 7/2(8/15 - 1/2)
= 7/2(16 - 15/30)
= 7/2*1/30
= 7/60
Therefore after evaluating the value of triple integral is 7/60.
Learn more about the triple integral here:
https://brainly.com/question/2289273
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