Calculate the Iterated Integral $\int _ { - 1 } ^ { 2 } \left( \int _ { 0 } ^ { 1 / x ^ { 2 } } x ^ { 3 } e ^ { x ^ { 3 } y } d y \right)$

question 35

Short Answer

Calculate the iterated integral $\int _ { - 1 } ^ { 2 } \left( \int _ { 0 } ^ { 1 / x ^ { 2 } } x ^ { 3 } e ^ { x ^ { 3 } y } d y \right)$ dx.
Enter your answer exactly in the form $e ^ { a }$ ± b - $\mathrm { e } ^ { \mathrm { C } }$ .

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Definitions:

Split-off

A point in the production process where multiple products are generated from a common input.

Avoidable Cost

A cost that can be eliminated if a particular business decision is made.

Variable Production Cost

Costs that vary directly with the volume of production, including direct materials and direct labor, and sometimes variable portions of manufacturing overhead.

Stamping Machine

A machine used in manufacturing to shape or cut materials using dies and high pressure.