Evaluate $\int x ^ { 3 } \left( x ^ { 2 } - 3 \right) ^ { 7 } d x$

question 30

Multiple Choice

Evaluate $\int x ^ { 3 } \left( x ^ { 2 } - 3 \right) ^ { 7 } d x$ .

• A) \(\frac { \left( x ^ { 2 } - 3 \right) ^ { 8 } x ^ { 3 } } { 24 } + C\)
• B) \(\frac { x ^ { 2 } } { 16 } \left( x ^ { 2 } - 3 \right) ^ { 8 } + C\)
• C) \(\frac { x ^ { 2 } } { 16 } \left( x ^ { 2 } - 3 \right) ^ { 8 } - \frac { 1 } { 144 } \left( x ^ { 2 } - 3 \right) ^ { 9 } + C\)
• D) \(\frac { x ^ { 2 } } { 16 } \left( x ^ { 2 } - 3 \right) ^ { 8 } - \frac { 1 } { 72 } \left( x ^ { 2 } - 3 \right) ^ { 9 } + C\)

---

Definitions:

Fixed Overhead Volume

refers to the portion of fixed overhead costs that is associated with the production volume, used in calculating efficiency and profitability.

Standard Machine-Hours

A measure used in manufacturing to allocate costs to products based on the estimated number of hours the machinery is used.

Actual Output

Actual output is the quantity of finished goods or services produced by a company in a specific period.

Overapplied

A situation in cost accounting where the allocated manufacturing overhead for a period exceeds the actual manufacturing overhead costs incurred.