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:

Subatomic Particles

Particles that are smaller than an atom, including protons, neutrons, and electrons, which are the basic building blocks of atoms.

Elements

Elements are fundamental components or substances that cannot be broken down into simpler forms by chemical means.

Scientific Theories

Well-substantiated explanations of some aspect of the natural world, based on a body of empirical evidence and subjected to the scientific method.

Ever-living Fire

In Heraclitean philosophy, it symbolizes the fundamental principle of the universe, denoting change and the dynamic process of becoming.