Integration by Parts for Complex Integrals

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Homework Help Overview

The discussion revolves around the integration of the function x^12 sin(x) with a focus on integration by parts and potential alternative methods such as recurrence relations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the validity of a proposed solution and suggest checking work through differentiation. Some consider the use of recurrence relations, while others discuss the repeated application of integration by parts.

Discussion Status

The discussion is active, with participants offering different approaches and questioning the correctness of initial attempts. There is no explicit consensus, but various methods are being explored.

Contextual Notes

Participants are encouraged to check their work and consider different strategies for solving the integral, indicating a focus on understanding the integration process rather than arriving at a final answer.

donglepuss
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Homework Statement
integral of x^12 sinx dx
Relevant Equations
answer: x^12 -cosx - 12x^11 sinx - cosx (132x^11/11)
integral of x^12 sinx dx = x^12 -cosx - 12x^11 sinx - cosx (132x^11/11)
 
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donglepuss said:
Homework Statement: integral of x^12 sinx dx
Homework Equations: answer: x^12 -cosx - 12x^11 sinx - cosx (132x^11/11)

integral of x^12 sinx dx = x^12 -cosx - 12x^11 sinx - cosx (132x^11/11)
No, it's not.
However, you should get into the habit of checking your work when you have an integration problem. Just differentiate your answer, and if it is correct, you'll end up with the original integrand.
 
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Might I suggest trying to use recurrence relations? I'm not sure if it's the best idea, though.

In any case, what I did was set ##I(n)=\int x^n \sin(x) \ dx## where ##n## is a positive integer.
 
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It looks like you are trying to use integration by parts repeatedly, which should work if you do it right. As a reminder:
$$\int udv = uv - \int vdu$$
 
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