Answer:
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
- Integrals
Integration Rule [Fundamental Theorem of Calculus 1]:
Integration Property [Multiplied Constant]:
U-Substitution
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Integrate Pt. 1</u>
<em>Identify variables for u-substitution.</em>
- Set <em>u</em>:
- [<em>u</em>] Differentiate [Basic Power Rule, Derivative Properties]:
- [Bounds] Switch:
<u>Step 3: Integrate Pt. 2</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
- [Integral] U-Substitution:
- [Integral] Exponential Integration:
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
- Simplify:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration