Answer:
General Formulas and Concepts:
<u>Algebra I</u>
<u>Calculus</u>
Antiderivatives - integrals/Integration
Integration Constant C
U-Substitution
Integration Property [Multiplied Constant]:
Trig Integration:
Step-by-step explanation:
<u>Step 1: Define</u>
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<u>Step 2: Integrate Pt. 1</u>
- [Integral] Factor fraction denominator:
- [Integral] Integration Property - Multiplied Constant:
<u>Step 3: Identify Variables</u>
<em>Set up u-substitution for the arctan trig integration.</em>
<u>Step 4: Integrate Pt. 2</u>
- [Integral] Substitute u-du:
- [Integral] Trig Integration:
- [Integral] Simplify:
- [integral] Multiply:
- [Integral] Back-Substitute:
Topic: AP Calculus AB
Unit: Integrals - Arctrig
Book: College Calculus 10e
Answer:
Step-by-step explanation:
Given the expression , apply natural logarithm to both sides. Then:
Remember that according the the properties of logarithms:
Then:
Apply distributive property and solve for "x". Then you get:
Answer:
113.1
Step-by-step explanation:
Volume of sphere = × π × r²
Volume of sphere = × π × 3²
Volume of sphere = × π × 9
Volume of sphere = × 9 π
Volume of sphere = 113.1
24 square units
because 8*3=24 square units
Answer:
cos²x
Step-by-step explanation:
(a-b)(a+b)=a²-b²
sin²x+cos²x=1 => cos²x=1-sin²x
(1 − sin x)(1 + sin x)=1-sin²x=cos²x