Question

What is the definite integral of #x^3# from 1 to 2?

Answer 1

`\displaystyle \int\limits^2_1 {x^3} \, dx = (15)/(4)`

General Formulas and Concepts:

Calculus

Integration

• Integrals

Integration Rule [Reverse Power Rule]:
`\displaystyle \int {x^n} \, dx = (x^(n + 1))/(n + 1) + C`

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

Explanation:

Step 1: Define

Identify

`\displaystyle \int\limits^2_1 {x^3} \, dx`

Step 2: Integrate

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

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

Unit: Integration