How to integrate this?

Question

Evaluate the following definite integral,

f(x,y)=max(x,y), over the region [(x,y): 0<=x<=1 ,0<=y<=1]

Also what do they mean by max(x,y)?

Answer 1

max(x, y) means the greater of x &amp; y so

max(x, y) = y if y &gt; x

               = x otherwise

so the surface is symmetrical about the line x = y

so integrate over x from 0 to 1 and y from 0 to x of the function x and then multiply by 2 would get the answer..