Set Up the Definite Integral That Gives the Area of the Region

question 17

Multiple Choice

Set up the definite integral that gives the area of the region bounded by the graphs. $\begin{array} { l } f ( x ) = ( x - 4 ) ^ { 3 } \\g ( x ) = x - 4\end{array}$

• A) \(\int _ { 3 } ^ { 4 } \left( ( x - 4 ) - ( x - 4 ) ^ { 3 } \right) d x + \int _ { 4 } ^ { 5 } \left( ( x - 4 ) ^ { 3 } - ( x - 4 ) \right) d x\)
• B) \(\int _ { - 1 } ^ { 0 } \left( ( x - 4 ) + ( x - 4 ) ^ { 3 } \right) d x + \int _ { 0 } ^ { 1 } \left( ( x - 4 ) ^ { 3 } + ( x - 4 ) \right) d x\)
• C) \(\int _ { - 1 } ^ { 0 } \left( ( x - 4 ) ^ { 3 } - ( x - 4 ) \right) d x + \int _ { 0 } ^ { 1 } \left( ( x - 4 ) - ( x - 4 ) ^ { 3 } \right) d x\)
• D) \(\int _ { 3 } ^ { 4 } \left( ( x - 4 ) ^ { 3 } - ( x - 4 ) \right) d x + \int _ { 4 } ^ { 5 } \left( ( x - 4 ) - ( x - 4 ) ^ { 3 } \right) d x\)
• E) \(\int _ { 3 } ^ { 4 } \left( ( x - 4 ) ^ { 3 } + ( x - 4 ) \right) d x + \int _ { 4 } ^ { 5 } \left( ( x - 4 ) + ( x - 4 ) ^ { 3 } \right) d x\)

---

Definitions:

Consumption Method

An accounting practice that records the cost of goods sold at the time they are consumed or sold, as opposed to when they are purchased.

Office Supplies

Items needed for the daily operations of a business, such as pens, paper, and staplers.

Government-Wide Financial Statements

Comprehensive financial reports that present the financial position and results of operations of all governmental activities and entities.

Debt Service Fund

A fund established to account for the accumulation of resources for, and the payment of, long-term debt principal and interest.