Question

Let S ⊆ $\Re$ be the tetrahedron having vertices (0, 0, 0), (0, 1, 1), (1, 2, 3), and (−1, 0, 1).

Let f : $\Re ^{3}$ → $\Re ^{}$ be the function defined by f(x, y, x) = x − 2y + 3z.

Using the change of variables theorem,

rewrite $\int_s f$ as an integral over a 3-rectangle, then use Fubini’s theorem to evaluate the integral.

Answer 1

ANSWER:-
ô C -25 [ the given information is S; of (2, 4, Z) = x-2y+32 change of variables x = 5, y =5, zat - d (hy,z) dir, sit) dk dor da ds dt šlo stato dy dor dt ds oco dt ds dt dz dt dor = 1 > = 8/J (1-25 + 3x) de ds de JU 127-28+3+) dt ds da 119 Inros oo O lor - |-པོ་-S laros 11 lnres ds dri + 3 (+2 I 1-5 I1 = (1-0-5)-2511-4-5) + 3 (1-21-53% ds da. [1+²+52-29-25€ r- r-rs-25+255 +252 225) dsda oo

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