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Answer:
General Formulas and Concepts:
<u>Pre-Calculus</u>
- Unit Circle
- Trig Graphs
<u>Calculus</u>
- Limits
- Limit Rule [Variable Direct Substitution]:
- Integrals
- Integration Rule [Fundamental Theorem of Calculus 1]:
- Trig Integration
- Improper Integrals
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Integrate</u>
- [Improper Integral] Rewrite:
- [Integral] Trig Integration:
- [Integral] Evaluate [Integration Rule - FTC 1]:
- Evaluate trig:
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
Since we are dealing with infinity of functions, we can do a numerous amount of things:
- Since -sin(x) is a shift from the parent graph sin(x), we can say that -sin(∞) = sin(∞) since sin(x) is an oscillating graph. The values of -sin(x) already have values in sin(x).
- Since sin(x) is an oscillating graph, we can also say that the integral actually equates to undefined, since it will never reach 1 certain value.
∴
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Improper Integrals
Book: College Calculus 10e