Answer:
[tex]\displaystyle A = 12[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Algebra I
- Functions
- Function Notation
- Graphing
Calculus
Integrals
- Definite Integrals
- Area under the curve
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
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 = x
Interval: x = 1 to x = 5
Step 2: Sort
Graph the function. See Attachment.
Bounds of Integration: [1, 5]
Step 3: Find Area
- Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^5_1 {x} \, dx[/tex]
- [Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = \frac{x^2}{2} \bigg| \limits^5_1[/tex]
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle A = 12[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
