- #1
Integration by Parts Homework: Get Help Now
- Thread starter uzman1243
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Homework Help Overview
The discussion revolves around the application of integration by parts in the context of integrating sine functions raised to a power. Participants are exploring how to approach the problem and clarify the nature of the function involved.
Discussion Character
- Exploratory, Conceptual clarification, Problem interpretation
Approaches and Questions Raised
- Some participants express uncertainty about how to initiate the problem, particularly regarding the use of integration by parts. Others suggest examining specific cases to identify patterns and question the definitions and roles of the variables involved.
Discussion Status
The discussion is active, with participants offering hints and questioning assumptions. There is no explicit consensus yet, but some guidance has been provided regarding potential approaches to the problem.
Contextual Notes
Participants note the absence of specific equations and express confusion about the terminology used, particularly regarding the classification of the function as a sum versus a function of an exponent.
- #2
SteamKing
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First of all, I(n) is not a sum. I is a function which depends on the exponent of the sine function in the integrand.
You might try to determine what I(n) is for some discrete values of n, like n = 2, 3, 4, etc. and see if a pattern emerges.
You might try to determine what I(n) is for some discrete values of n, like n = 2, 3, 4, etc. and see if a pattern emerges.
- #3
SammyS
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What sum ?uzman1243 said:Homework Statement
Homework Equations
N/A
The Attempt at a Solution
I can't even begin the attempt because I don't know how you could use intergration by parts for this sum in the first place.
Can you help me out?
Let u = sin(n-1)(x), and dv = sin(x) dx
(The King beat me by fractions of a minute!)
- #4
lurflurf
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hint
$$\int\! \sin^n(x) \, \mathrm{d}x=\int\! \sin^{n-2}(x)\sin^{2}(x) \, \mathrm{d}x=\int\! \sin^{n-2}(x)\big(1-\cos^{2}(x)\big) \, \mathrm{d}x$$
$$\int\! \sin^n(x) \, \mathrm{d}x=\int\! \sin^{n-2}(x)\sin^{2}(x) \, \mathrm{d}x=\int\! \sin^{n-2}(x)\big(1-\cos^{2}(x)\big) \, \mathrm{d}x$$
- #5
mafagafo
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This does not look like precalculus.
- #6
uzman1243
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SammyS said:
Lol. He did.
Anyways, can you tell me why sin(n-1)(x)?
- #7
SammyS
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(n-1) is half way from n to (n-2) .uzman1243 said:
Try it and see what happens !
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