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Vera_Pavlovna [14]
3 years ago
8

Please help me with this function on a closed interval!

Mathematics
1 answer:
Softa [21]3 years ago
5 0

Answer:

(E) 13

General Formulas and Concepts:

<u>Pre-Algebra</u>

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<u> </u>

<u>Algebra I</u>

  • Functions
  • Function Notation

<u>Calculus</u>

Antiderivatives - Integrals

Integration Rule [Fundamental Theorem of Calculus 1]:                                      \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

Integration Rule [Fundamental Theorem of Calculus 2]:                                     \displaystyle \frac{d}{dx}[\int\limits^x_a {f(t)} \, dt] = f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<u />\displaystyle \int\limits^4_0 {f'(t)} \, dt = 8<u />

<u />\displaystyle f(4) = \text{unknown}<u />

<u />

<u>Step 2: Integrate</u>

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

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

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