Originally Posted by

**Opalg** The essential thing here is to DRAW A DIAGRAM of the region. It is bounded by the x- and y-axes and the line y = 4 – x. __Draw that diagram before reading any further.__

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Done that? You should have drawn a triangular region. Now imagine that region sliced by vertical lines, which each correspond to a fixed value of x. For each value of x between x=0 and x=4, the line will pass through the region (if x<0 or x>4 then the line will miss the region altogether). The section of line within the region goes from y=0 up to y=4–x. So the (inner) y integral should go from 0 to 4–x and the (outer) x integral will go from 0 to 4.