Evaluate the triple integral \int_0^5 \int_0^{\frac{y}{2}} \int_{\frac{2z-y}{2}}^{\frac{y}{2}+5} f(x, y, z)dxdydz where $f(x, y, z) = z + \frac{z}{3}$,
$u = \frac{2x-y}{2}$, $v = \frac{y}{2}$ and $w = \frac{z}{3}$.
Triple Integral
Region R
Remember that:
$\iiint_R F(x, y, z)dV = \iiint_C H(u, v, w)|J(u, v, w)|dudvdu$
$u$ lower limit = 0
$u$ upper limit = 5
$v$ lower limit = 0
$v$ upper limit = $\frac{5}{2}$
$w$ lower limit = 0
$w$ upper limit = $\frac{5}{3}$
$H(u, v, w) = $
$|J(u, v, w)| =
$\iiint_C H(u, v, w)|J(u, v, w)|dudvdu = $
Hint: Review the calculation of the partial derivatives
