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

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To integrate ax on the plane y=7, it is essential to recognize that ax is a constant unit vector in the x direction, allowing it to be factored out of the integral. The user is unsure about determining the limits of integration for x and z, as the problem only specifies the plane y=7 without detailing the region of integration. To proceed, one must define the bounds for x and z based on the specific area of interest within that plane. Understanding the context of the integration region is crucial for setting these limits correctly. Clarifying the integration region will enable a complete solution to the problem.
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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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