Double integral question: Evaluating Integrals with Sinusoidal Functions

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Homework Help Overview

The discussion revolves around evaluating double integrals involving sinusoidal functions, specifically focusing on the integration of sin(x^2) and the interpretation of variables and limits within the integrals.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to understand how to integrate sin(x^2) and questions the meaning of the variable R in the context of the integrals. Some participants inquire about the integration of x*sin(x^2) and clarify the presence of x in the limits of integration.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the integral setup and the roles of variables. Some guidance has been offered regarding the integration process, but no consensus has been reached on the overall approach.

Contextual Notes

Participants are navigating the complexities of double integrals and the specific roles of variables and limits, with some information potentially missing from the original problem statement.

engineer_dave
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Double integral question...

Homework Statement



Evaluate the integrals shown ( I have attached the file with the integral).

Homework Equations





The Attempt at a Solution



Ok, for the first one, can you tell me how I integrate sin x^2...?? which method should i use? And for the second one, I don't really understand what the R is. What do u have to do to find the values next to to the integrand. Thanks!
 

Attachments

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Can you integrate x*sin(x^2)?
 
yea but this doesn't have an x in front of it
 
any helpers lol??
 
Then I have no idea.
 
x is in the limits of the dy integration. Integrating sin(x^2) dy gives y*sin(x^2). Now put in the y limits THEN integrate dx. See, it does have an x in front of it.
 

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