Math Help - Calc III: Triple Integral Set Up

1. Calc III: Triple Integral Set Up

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?

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

2. The set up is correct