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Please help me with this function on a closed interval!

Please Help Me With This Function On A Closed Interval class=

Sagot :

Space

Answer:

(E) 13

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. 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

  1. [Integral] Evaluate [Integration Rule - FTC 1 and 2]:                                     [tex]\displaystyle \int\limits^4_0 {f'(t)} \, dt = f(4) - f(0)[/tex]
  2. [Integral] Substitute in variables [Given/Table]:                                           [tex]\displaystyle 8 = f(4) - 5[/tex]
  3. [Addition Property of Equality] Isolate f(4):                                                   [tex]\displaystyle 13 = f(4)[/tex]
  4. 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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