Answer:

General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
![\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)](https://img.qammunity.org/2019/formulas/mathematics/high-school/h3h81fknzks3m5lkzvmdwrmpof8mpsbacs.png)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
Integration Rule [Fundamental Theorem of Calculus 1]:

Integration Property [Multiplied Constant]:

U-Substitution
Explanation:
Step 1: Define
Identify

Step 2: Integrate Pt. 1
Identify variables for u-substitution.
- Set u:

- [u] Differentiate [Basic Power Rule, Derivative Properties]:

- [Bounds] Switch:

Step 3: Integrate Pt. 2
- [Integral] Rewrite [Integration Property - Multiplied Constant]:

- [Integral] U-Substitution:

- [Integral] Trigonometric Integration:
![\displaystyle \int\limits^{(\pi)/(24)}_0 {\cos (12x)} \, dx = (1)/(12)[-sin(u)] \bigg| \limits^{(\pi)/(2)}_0](https://img.qammunity.org/2019/formulas/mathematics/college/8gn2fwlx9vtfvjn4t1fa040uwaegeeyxj0.png)
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:

- Simplify:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration