A very thin 1" x 1" square tile is painted purple. The paint mass density increases steadily from one corner to the opposite corner starting at 0 oz./sq. inch and ending with 1 oz./sq. inch. Where
a. Are the corners of the tile painted with different shades of purple?
b. What is the average mass density of the paint on the tile?
c. What is the total mass of paint on the tile?
d. How does the mass density of the paint change from one corner to the opposite corner?