Answer:
General Formulas and Concepts:
<u>Pre-Calculus</u>
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Integration
- Integrals
- Definite/Indefinite Integrals
- Integration Constant C
Integration Rule [Reverse Power Rule]: 
Integration Rule [Fundamental Theorem of Calculus 1]: 
U-Substitution
- Trigonometric Substitution
Reduction Formula: 
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 (trigonometric substitution).</em>
- Set <em>u</em>:

- [<em>u</em>] Differentiate [Trigonometric Differentiation]:

- Rewrite <em>u</em>:

<u>Step 3: Integrate Pt. 2</u>
- [Integral] Trigonometric Substitution:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[1 - sin^2(u)]^\Big{\frac{3}{2}} \, du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bcos%28u%29%5B1%20-%20sin%5E2%28u%29%5D%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%5C%2C%20du)
- [Integrand] Rewrite:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[cos^2(u)]^\Big{\frac{3}{2}} \, du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bcos%28u%29%5Bcos%5E2%28u%29%5D%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%5C%2C%20du)
- [Integrand] Simplify:

- [Integral] Reduction Formula:

- [Integral] Simplify:

- [Integral] Reduction Formula:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg|\limits^a_b + \frac{3}{4} \bigg[ \frac{2 - 1}{2}\int\limits^a_b {cos^{2 - 2}(u)} \, du + \frac{cos^{2 - 1}(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B2%20-%201%7D%7B2%7D%5Cint%5Climits%5Ea_b%20%7Bcos%5E%7B2%20-%202%7D%28u%29%7D%20%5C%2C%20du%20%2B%20%5Cfrac%7Bcos%5E%7B2%20-%201%7D%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- [Integral] Simplify:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}\int\limits^a_b {} \, du + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B2%7D%5Cint%5Climits%5Ea_b%20%7B%7D%20%5C%2C%20du%20%2B%20%5Cfrac%7Bcos%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- [Integral] Reverse Power Rule:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}(u) \bigg| \limits^a_b + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B2%7D%28u%29%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7Bcos%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- Simplify:

- Back-Substitute:

- Simplify:

- Rewrite:

- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
23.4 ft2
Step-by-step explanation:
jvuctctctcrxrxrxrxrxr
Umm im pretty sure d= -3x im not to sure
Answer:
Step-by-step explanation:
2/9x+3>4 5/9
Subtract
2/9x>7 5/9
Divide by 2/9
x>34
As none of the number lines represent this data, the question was written incorrectly, or there is more information.
First thing you need to do is distributive property and that will give you
7-56-7x=-14+4x then combine like terms which will then give you
-49-7x=-14+4x Next get your letters on the left do that by subtracting 4x which will give you -49-11x=-14. After that you will add 49 to both sides which will give you
-11x= 35. Divide by -11 to get x=3.18