Use Cylindrical Coordinates to Evaluate the Triple Integral $\iiint _ { { E } } x e ^ { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 2 } }dV$

Short Answer

Use cylindrical coordinates to evaluate the triple integral $\iiint _ { { E } } x e ^ { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 2 } }dV$ where E is the solid that lies between the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 8$ and $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 18$ in the first octant.