B. -15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Left to Right
Distributive Property
Equality Properties
Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality
Calculus
Integrals
Integration Rule [Reverse Power Rule]:
Integration Property [Swapping Limits]:
Integration Property [Multiplied Constant]:
Integration Property [Addition/Subtraction]:
Integration Property [Splitting Integral]:
Integration Rule [Fundamental Theorem of Calculus 1]:
Step-by-step explanation:
Step 1: Define
Step 2: Redefine
Manipulate the given integrals.
[Integrals] Combine [Integration Property - Splitting Integral]:
[Integrals] Rewrite:
[Integrals] Substitute in variables:
[Integrals] Rewrite [Integration Property - Swapping Limits]:
[Integrals] [Division Property of equality] Isolate integral:
[Integrals] [Distributive Property] Distribute negative:
Step 3: Solve
[Integral] Rewrite [Integration Property - Addition]:
[Integral] Rewrite [Integration Property - Multiplied Constant]:
[Integral] Substitute in integral:
[Integral] Integrate [Integration Rule - Reverse Power Rule]:
[Integral] Evaluate [Integration Rule - FTC 1]:
[Integral] (Parenthesis) Simplify:
[Integral] (Parenthesis) Add:
[Integral] Multiply:
[Integral] [Subtraction Property of Equality] Subtract 16 on both sides:
[Integral] [Division Property of Equality] Divide 2 on both sides:
[Integral] [Addition Property of Equality] Isolate z term:
[Integral] [Division Property of Equality] Isolate z:
[Integral] Back-Substitute:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e