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Sagot :
Answer:
(E) 13
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Algebra I
- Functions
- Function Notation
Calculus
Antiderivatives - Integrals
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Rule [Fundamental Theorem of Calculus 2]: [tex]\displaystyle \frac{d}{dx}[\int\limits^x_a {f(t)} \, dt] = f(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits^4_0 {f'(t)} \, dt = 8[/tex]
[tex]\displaystyle f(4) = \text{unknown}[/tex]
Step 2: Integrate
- [Integral] Evaluate [Integration Rule - FTC 1 and 2]: [tex]\displaystyle \int\limits^4_0 {f'(t)} \, dt = f(4) - f(0)[/tex]
- [Integral] Substitute in variables [Given/Table]: [tex]\displaystyle 8 = f(4) - 5[/tex]
- [Addition Property of Equality] Isolate f(4): [tex]\displaystyle 13 = f(4)[/tex]
- Rewrite: [tex]\displaystyle f(4) = 13[/tex]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
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