Express the integral \(\displaystyle \iiint_E f(x,y,z) dV\) as an iterated integral in six different ways, where E is the solid bounded by \(z =0, x = 0, z = y - 8 x\) and \(y = 24\text{.}\)
1. \(\displaystyle \int_a^b
\int_{g_1(x)}^{g_2(x)} \int_{h_1(x,y)}^{h_2(x,y)}f(x,y,z) dz dy dx\)
\(a =\) \(b =\)
\(g_1(x) =\) \(g_2(x) =\)
\(h_1(x,y) =\) \(h_2(x,y) =\)
2. \(\displaystyle \int_a^b
\int_{g_1(y)}^{g_2(y)} \int_{h_1(x,y)}^{h_2(x,y)}f(x,y,z) dz dx dy\)
\(a =\) \(b =\)
\(g_1(y) =\) \(g_2(y) =\)
\(h_1(x,y) =\) \(h_2(x,y) =\)
3. \(\displaystyle \int_a^b
\int_{g_1(z)}^{g_2(z)} \int_{h_1(y,z)}^{h_2(y,z)}f(x,y,z) dx dy dz\)
\(a =\) \(b =\)
\(g_1(z) =\) \(g_2(z) =\)
\(h_1(y,z) =\) \(h_2(y,z) =\)
4. \(\displaystyle \int_a^b
\int_{g_1(y)}^{g_2(y)} \int_{h_1(y,z)}^{h_2(y,z)}f(x,y,z) dx dz dy\)
\(a =\) \(b =\)
\(g_1(y) =\) \(g_2(y) =\)
\(h_1(y,z) =\) \(h_2(y,z) =\)
5. \(\displaystyle \int_a^b
\int_{g_1(x)}^{g_2(x)} \int_{h_1(x,z)}^{h_2(x,z)}f(x,y,z) dy dz dx\)
\(a =\) \(b =\)
\(g_1(x) =\) \(g_2(x) =\)
\(h_1(x,z) =\) \(h_2(x,z) =\)
6. \(\displaystyle \int_a^b
\int_{g_1(z)}^{g_2(z)} \int_{h_1(x,z)}^{h_2(x,z)}f(x,y,z) dy dx dz\)
\(a =\) \(b =\)
\(g_1(z) =\) \(g_2(z) =\)
\(h_1(x,z) =\) \(h_2(x,z) =\)