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Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right<u> </u>
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u> </u>
<u>Algebra I</u>
- Terms/Coefficients
- Functions
- Function Notation
- Graphing
- Solving systems of equations
<u>Calculus</u>
Area - Integrals
Integration Rule [Reverse Power Rule]:
Integration Rule [Fundamental Theorem of Calculus 1]:
Integration Property [Addition/Subtraction]:
Area of a Region Formula:
Step-by-step explanation:
*Note:
<em>Remember that for the Area of a Region, it is top function minus bottom function.</em>
<u />
<u>Step 1: Define</u>
f(x) = x²
g(x) = x⁶
Bounded (Partitioned) by x-axis
<u>Step 2: Identify Bounds of Integration</u>
<em>Find where the functions intersect (x-values) to determine the bounds of integration.</em>
Simply graph the functions to see where the functions intersect (See Graph Attachment).
Interval: [-1, 1]
Lower bound: -1
Upper Bound: 1
<u>Step 3: Find Area of Region</u>
<em>Integration</em>
- Substitute in variables [Area of a Region Formula]:
- [Area] Rewrite [Integration Property - Subtraction]:
- [Area] Integrate [Integration Rule - Reverse Power Rule]:
- [Area] Evaluate [Integration Rule - FTC 1]:
- [Area] Subtract:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Area Under the Curve - Area of a Region (Integration)
Book: College Calculus 10e
