Answer:
[tex]\displaystyle A = \int\limits^{2\sqrt{2} - 1}_{-(2\sqrt{2} + 1)} {(-x^2 - 2x + 7)} \, dx[/tex]
General Formulas and Concepts:
Calculus
Integration
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = -x² + 4
y = 2x - 3
Step 2: Identify
Graph functions and find region and bounds of integration.
Bounds: [-(2√2 + 1), 2√2 - 1]
Step 3: Find Area
- Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^{2\sqrt{2} - 1}_{-(2\sqrt{2} + 1)} {[-x^2 + 4 - (2x - 3)]} \, dx[/tex]
- Simplify: [tex]\displaystyle A = \int\limits^{2\sqrt{2} - 1}_{-(2\sqrt{2} + 1)} {(-x^2 - 2x + 7)} \, dx[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
