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.

Question

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.

Quizplus · Accepted Answer

The Answer is

\frac { \pi } { 18 } \left( e ^ { 324 } - e ^ { 64 } \right)

Use Cylindrical Coordinates to Evaluate the Triple Integral ∭Exe(x2+y2+z2)2dV\iiint _ { { E } } x e ^ { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 2 } }dV∭E​xe(x2+y2+z2)2dV

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