Respuesta :

Space

Answer:

[tex]\displaystyle \int\limits^2_1 {x^3} \, dx = \frac{15}{4}[/tex]

General Formulas and Concepts:

Calculus

Integration

  • Integrals

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]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^2_1 {x^3} \, dx[/tex]

Step 2: Integrate

  1. [Integral] Reverse Power Rule:                                                                    [tex]\displaystyle \int\limits^2_1 {x^3} \, dx = \frac{x^4}{4} \bigg| \limits^2_1[/tex]
  2. Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:          [tex]\displaystyle \int\limits^2_1 {x^3} \, dx = \frac{15}{4}[/tex]

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

Unit: Integration

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