Evaluate the Integral Using the Given Substitution $$\int x ^ { 4 } \left( x ^ { 5 } - 9 \right) ^ { 4 } d x , u = x ^ { 5 } - 9$$

question 289

Multiple Choice

Evaluate the integral using the given substitution.
- $$\int x ^ { 4 } \left( x ^ { 5 } - 9 \right) ^ { 4 } d x , u = x ^ { 5 } - 9$$

• A) \(\frac { 1 } { 25 } \left( x ^ { 5 } - 9 \right) ^ { 5 } + C\)
• B) \(\frac { 1 } { 5 } \left( x ^ { 5 } - 9 \right) ^ { 5 } + C\)
• C) \(\frac { 1 } { 15 } \left( x ^ { 5 } - 9 \right) ^ { 3 } + C\)
• D) \(\frac { 1 } { 25 } x ^ { 25 } - 9 + C\)

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Definitions:

Production Increases

A rise in the amount or level of output that a production system generates over a specific period.

High-low Method

A cost accounting technique used to estimate variable and fixed costs based on the highest and lowest levels of activity within a given period.

Variable Cost

Costs that vary directly with the level of production or sales volume. They include raw materials, labor directly involved in production, and sales commissions.

Total Fixed Costs

The sum of all costs that remain constant regardless of the level of production or sales.