Answer:
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
- Integrals
Integration Rule [Reverse Power Rule]:
Integration Rule [Fundamental Theorem of Calculus 1]:
Integration Property [Addition/Subtraction]:
U-Substitution
Area of a Region Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Identify</u>
<em>Graph the systems of equations - see attachment.</em>
Top Function:
Bottom Function:
Bounds of Integration: [-1.529, 1.718]
<u>Step 3: Integrate Pt. 1</u>
- Substitute in variables [Area of a Region Formula]:
- [Integral] Rewrite [Integration Property - Addition/Subtraction]:
- [Right Integral] Integration Rule [Reverse Power Rule]:
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
<u>Step 4: Integrate Pt. 2</u>
<em>Identify variables for u-substitution.</em>
- Set <em>u</em>:
- [<em>u</em>] Basic Power Rule [Derivative Rule - Addition/Subtraction]:
- [Limits] Switch:
<u>Step 5: Integrate Pt. 3</u>
- [Integral] U-Substitution:
- [Integral] Integration Rule [Reverse Power Rule]:
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
- Simplify:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
