How do I integrate ax on the plane y=7?

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    Integral Vector
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Homework Help Overview

The discussion revolves around integrating the expression ax over the plane defined by y=7. Participants are exploring the implications of this integration in a multivariable context.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of ax, questioning whether it is constant over the integration region and how that affects the integration process. There are inquiries about the limits of integration for the variables x and z.

Discussion Status

The conversation is ongoing, with some participants providing hints about treating ax as a constant and questioning the region of integration. There is a lack of consensus on how to define the limits for the integration.

Contextual Notes

Participants note that the problem specifies the plane y=7 but do not have additional information about the region of integration, which is causing uncertainty in determining the limits for x and z.

Melawrghk
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Homework Statement



doubleintegral.jpg


The Attempt at a Solution


I get parts a and b, but I don't know what to do for part c.
I can write a double integral with dx and dz (because y is constant) and substitute y=7 in, but I'm not sure how to integrate ax...

Any hints would be appreciated.
 
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First, is ax constant over the integration region? If so, you can pull it out of the integral, just as with a numeric constant.

If it's not constant, you'd need to find a way to express it in terms of things (i.e. other unit vectors) that are constant.
 
Well I guess ax is a unit vector in the x direction, so it must be constant.

But how do I figure out the limits of integration for x and z?
 
Well, what's the region of integration?
 
I don't know, it just says plane y=7.
 

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