Evaluating 2D Integrals: f(x,y)=min(x,y)

[rgalvan2]

Homework Statement

Evaluate the following definite two-dimensional integrals over the specified domains of integration.

f(x,y)=min(x,y), over the region {(x,y) : 0 $$\leq$$ x $$\leq$$ 2, 0 $$\leq$$ y $$\leq$$ 1}

Homework Equations

The Attempt at a Solution

I'm not even sure where to start because I'm not sure what the problem even means by f(x,y)=min(x,y). HELP!

 

[dx]

min(x,y) means minimum of x and y. For example, in the region x < y, f(x,y) = x.

 

[rgalvan2]

So if I integrate first from 0 $$\leq$$ y $$\leq$$ 1 then the x bounds, my f(x,y)=y? I'm a little confused over this. I don't remember going over this in calculus and this homework is supposed to be a calculus review.

 

[dx]

Divide the region {(x,y) : 0 < x < 2, 0 < y < 1} into two parts, one where f(x,y) = x, and one where f(x,y) = y. Then do the usual double integration for the two regions separately.