Evaluate the Differential Is Exact $$\int _ { ( 0,0,0 ) } ^ { ( 3,7,9 ) } ( 3 x + 1 ) e ^ { 3 x } d x + z d y + y d z$$

question 57

Multiple Choice

Evaluate. The differential is exact.
- $$\int _ { ( 0,0,0 ) } ^ { ( 3,7,9 ) } ( 3 x + 1 ) e ^ { 3 x } d x + z d y + y d z$$

• A) \(3 \mathrm { e } ^ { 9 } + 64\)
• B) \(3 e ^ { 9 } + 63\)
• C) \(3 \mathrm { e } ^ { 9 } + 16\)
• D) 0

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Definitions:

Industry Supply Curve

A graphical representation that shows the relationship between the price of a good and the total output of the industry for that good.

Shutdown Point

The level of production and price where a company's revenue just covers its variable costs, below which it would be more economical for the firm to cease operations.

Average Variable Cost

The total variable costs of production divided by the quantity of output produced, representing the variable cost per unit of output.

Normal Rates

The standard or average prices, fees, or charges for goods, services, or financial transactions within a specific sector or economy.