Instructions state to find the average value of over the region .

with the region R being a triangle with vertices at (0,0), (0,1) and (1,1).

So the base formula for taking the average is:

Drawing the graph, I find it is a triangle anchored at the origin. I'm approaching it from the dy position so I have points from to and it's entering the region in question at and exiting the region at .

My double integral is as follows:

Here's where I run into trouble because I'm not sure how to use a U sub to my advantage on this problem. If I do so , well I don't have a Y in the function, but obviously I do have a 1, so how would I approach this problem? Would I do so I have:

Or would I do something different?