Conceptual double integral question

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Homework Help Overview

The problem involves evaluating a double integral of the function x²sin(y²) over a region R defined by the curves y = x³, y = -x³, and y = 8. Participants are discussing the setup of the integral limits and the implications of different approaches to defining the region of integration.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are comparing their methods for setting the limits of integration, specifically the inner integral limits. There is a question about why different setups yield the same result and whether one approach might be incorrect or incomplete.

Discussion Status

The discussion is ongoing with participants sharing their reasoning and questioning the validity of the book's approach compared to their own. Some guidance has been offered regarding the correctness of the methods used, but no consensus has been reached regarding the interpretation of the region.

Contextual Notes

There is a mention of potential confusion regarding the inclusion of negative regions in the setup of the integral, which may affect the interpretation of the area being integrated over.

Mdhiggenz
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Homework Statement



∫∫x2sin(y2)dA; R is the region that is bounded by y=x3
y=-x3, and y=8.

While working out the regions for this integral I set the inner integral to -y1/3 to y1/3. and the outer integral from 0 to 8. The book however set the inner integral from 0 to y1/3. However we both got the same answer, is there a reason for this?

Thanks

Higgenz


Homework Equations





The Attempt at a Solution

 
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Hi Mdhiggenz! :smile:
Mdhiggenz said:
While working out the regions for this integral I set the inner integral to -y1/3 to y1/3. and the outer integral from 0 to 8. The book however set the inner integral from 0 to y1/3. However we both got the same answer, is there a reason for this?

Either one of you made a mistake, or the book multiplied by 2 after integrating. :confused:
 
Hey Tim,

Yea the books answer is quite strange, the way I reasoned my answer is when I drew the graph R2: goes from -y^1/3 to positive y^1/3. Unless the book chose not to include the negative region.

Thoughts?
 
Your method looks fine. :confused:
 

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