Double integrals using polar co-ordinates

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Homework Help Overview

The discussion revolves around the application of double integrals using polar coordinates, specifically in the context of finding the volume of a solid defined by certain inequalities. Participants are exploring the conversion of Cartesian coordinates to polar coordinates and the implications for the limits of integration.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to convert the given inequalities into polar coordinates and graphed the resulting functions. They express confusion regarding the limits for theta after interpreting the graph. Other participants question the clarity of the problem statement and the nature of the region defined by the inequalities, with some noting that the shape described may not be a circle but rather a solid cylinder.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the original question and the interpretation of the inequalities. Some guidance is being offered regarding the nature of the geometric shapes involved, but there is no explicit consensus on the correct approach or interpretation yet.

Contextual Notes

There appears to be some missing information regarding the problem statement, as one participant notes an oversight in typing it up. Additionally, there is a discussion about the interpretation of the inequalities and their geometric implications, which may affect the setup of the integral.

Mdhiggenz
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Homework Statement



fp7dlf.jpg




Step 1) I put the following into polar coordinates
√(16-x2-y2)=√16-r2

Where r≤4

step 2 I solved for y in the original problem which is in the link

y≤√(4-x2)

step 3. I graphed the above function

step 4. I put the above function in polar coordinates getting

r≤2

So I already had an idea that the graph would be from

0≤r≤2 dr However my d(theta) was incorrect I got that it would be 0≤theta≤∏ as my interpretation of the graph shows. The answer however shows 0≤theta≤2∏

Which does't make much sense to me. Where did I got wrong?

Homework Equations





The Attempt at a Solution

 
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what is the actual question? :confused:
 
Upper left hand corner of the graph, the problem statement says Use a multiple integral and a convenient coordinate system to find the volume of the solid. I forgot to type it up I apologize.
 
i still don't get it

x2+ y2 ≤ 4 isn't a circle, it's a solid cylinder

anyway, show us how you found the line of interection​
 
Honestly I don't know I solved as if it was a circle.
 

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