Double Integral in open rectangle

[Nickfytas]

The exercise says to apply the mean value theorem in an open rectangle , but the theorem applies only in closed rectangle. If possible how to prove that it is the same in the open as in the closed rectangle

(The exercise in the image)

 

[HallsofIvy]

Do the problem on the closed interval. The boundary isn't going to contribute anything to the integral.

 

[Nickfytas]

Is there a mathematical explanation to why the integral in the same in the open as in the closed .?

 

[Deleted member 4993]

Is there a mathematical explanation to why the integral in the same in the open as in the closed .?

The reason was given in response #2 - The boundary isn't going to contribute anything to the integral

 

[Nickfytas]

Thank you!!