Not sure if this surface integral is right

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Homework Help Overview

The discussion revolves around a surface integral problem, specifically focusing on the integration over various faces of a prism. Participants are examining the correctness of the integration process and the handling of surface normals.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts manual integration of the surface integral, detailing the order of surfaces considered. Some participants question the correctness of the normal vector directions used in the integration process and suggest that errors may have occurred in the calculations.

Discussion Status

Participants are actively identifying potential errors in the original poster's approach, particularly regarding the signs of the normals and specific integration steps. There is no explicit consensus on the correctness of the final answer, but guidance has been offered regarding the normal directions.

Contextual Notes

There are indications of confusion regarding the integration setup and the treatment of surface normals, which may affect the overall solution. The original poster's final answer appears to differ from their initial calculations, suggesting ongoing uncertainty in the problem-solving process.

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Homework Statement


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The Attempt at a Solution



I did the manual integration of part (i) and got an answer of 5/6 instead, I'm not sure which part is wrong.. For the surfaces, I start off with the surface in the x-z plane, then the slanted plane, then the y-z plane, then the top of the prism and finally the bottom of the prism.

For the slanted plane, I projected it onto the x-z plane to do the integration..

Part (a)
2dtngx0.png

k2beox.png
 
Last edited:
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I see two errors in the face by face method.
You have the sign of the normal wrong in the first and third faces. The direction is always outwards.
For the second face, you correctly had ∫xy2+x2, but went wrong in the next line.
 
haruspex said:
I see two errors in the face by face method.
You have the sign of the normal wrong in the first and third faces. The direction is always outwards.
For the second face, you correctly had ∫xy2+x2, but went wrong in the next line.

Thanks! I will try again.
 
haruspex said:
I see two errors in the face by face method.
You have the sign of the normal wrong in the first and third faces. The direction is always outwards.
For the second face, you correctly had ∫xy2+x2, but went wrong in the next line.

Finally got the answer as 1/4 ! Thanks a lot!
 

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