Answer:

General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
Integration Rule [Reverse Power Rule]:

Integration Rule [Fundamental Theorem of Calculus 1]:

Integration Property [Addition/Subtraction]:
![\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx](https://img.qammunity.org/2022/formulas/mathematics/high-school/r5yh324r81plt97j3zrr5qi2xxczxlqi34.png)
U-Substitution
Area of a Region Formula:
![\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx](https://img.qammunity.org/2022/formulas/mathematics/college/uij08sp4x97gp23utcdwranet4linkrd6u.png)
Explanation:
Step 1: Define

Step 2: Identify
Graph the systems of equations - see attachment.
Top Function:

Bottom Function:

Bounds of Integration: [-1.529, 1.718]
Step 3: Integrate Pt. 1
- 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]:

Step 4: Integrate Pt. 2
Identify variables for u-substitution.
- Set u:

- [u] Basic Power Rule [Derivative Rule - Addition/Subtraction]:

- [Limits] Switch:

Step 5: Integrate Pt. 3
- [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