Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Antiderivatives - Integrals
Indefinite Integrals
U-Substitution
Integration Property [Multiplied Constant]:
Arctrig Integration [arctangent]:
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Integrate Pt. 1</u>
- [Integral] Rewrite:
<u>Step 3: Identify Variables</u>
<em>Identify variables for u-substitution of arctrig.</em>
- Set <em>u</em>:
- Differentiate [Basic Power Rule]:
- [Derivative] Simplify:
- [Derivative] Rewrite:
- Set <em>a</em>:
<u>Step 4: Integrate Pt. 2</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
- [Integral] U-Substitution:
- [Integral] Arctrig Integration [arctangent]:
- [Integral] Back-Substitute:
- [Integral] Divide:
- [Integral] Multiply:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration of Arctrig
Book: College Calculus 10e