There is a tetrahedron made with its z-intercept = 6, its y-intercept = 4, and its x-intercept = 4. x, y, and z are always positive. Calculate the integral of f(x,y,z) = e^(x + y + z) over the tetrahedron.

Are these limits and order of integration correct?

$\displaystyle \int_{0}^{4}\int_{0}^{4-x}\int_{0}^{6-3y/2-3x/2}e^{x+y+z}dzdydx

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