Answer:

General Formulas and Concepts:
<u>Algebra I</u>
- Functions
- Function Notation
- Graphing
<u>Calculus</u>
Integrals
Integration Rule [Reverse Power Rule]: 
Integration Rule [Fundamental Theorem of Calculus 1]: 
Integration Property [Multiplied Constant]: 
Integration Property [Addition/Subtraction]: ![\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%7D%20%5C%2C%20dx%20%3D%20%5Cint%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%5Cpm%20%5Cint%20%7Bg%28x%29%7D%20%5C%2C%20dx)
Shell Method: 
- [Shell Method] 2πx is the circumference
- [Shell Method] 2πxf(x) is the surface area
- [Shell Method] 2πxf(x)dx is volume
Step-by-step explanation:
<u>Step 1: Define</u>
y = x²
y = 0
x = 5
<u>Step 2: Identify</u>
<em>Find other information from graph.</em>
<em>See Attachment.</em>
Bounds of Integration: [0, 5]
<u>Step 3: Find Volume</u>
- Substitute in variables [Shell Method]:

- [Integrand] Multiply:

- [Integral] Integrate [Integration Rule - Reverse Power Rule]:

- Evaluate [Integration Rule - FTC 1]:

- Multiply:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e