Answer:
![\displaystyle A = \int\limits^{1.5}_0 {(x + 1)} \, dx + \int\limits^4_{1.5} {(4 - x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint%5Climits%5E%7B1.5%7D_0%20%7B%28x%20%2B%201%29%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E4_%7B1.5%7D%20%7B%284%20-%20x%29%7D%20%5C%2C%20dx)
General Formulas and Concepts:
<u>Algebra I</u>
- Functions
- Function Notation
- Points of Intersection
<u>Calculus</u>
Integrals - Area under the curve
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
y = x + 1
y = 4 - x
y = 0
x = 0
<u>Step 2: Identify Info</u>
<em>Graph the functions - See Attachment</em>
Bounds of Integration: [0, 4]
Point of Intersection: x = 1.5
<u>Step 3: Find Area</u>
- Set up [Integral - Area]:
![\displaystyle A = \int\limits^{1.5}_0 {(x + 1)} \, dx + \int\limits^4_{1.5} {(4 - x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint%5Climits%5E%7B1.5%7D_0%20%7B%28x%20%2B%201%29%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E4_%7B1.5%7D%20%7B%284%20-%20x%29%7D%20%5C%2C%20dx)
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration - Area under the curve
Book: College Calculus 10e