Question 1
In this paper, let $[x]$ denote the greatest integer not exceeding x. For examples, $[5]=5$, $[2.8]=2$, and $[-2.3]=-3$.
Find the area of the region R on the xy-plane consisting of the points (x,y) satisfying the equation $[x]+[y]=10$, where $0\le x\le 3$.
(Note: If you think that the region R does not have any area, enter your answer as “0”; if you think that the region R is unbounded, enter your answer as “99999”.)
Find the area of the region R on the xy-plane consisting of the points (x,y) satisfying the equation $[x]+[y]=10$, where $0\le x\le 3$.
(Note: If you think that the region R does not have any area, enter your answer as “0”; if you think that the region R is unbounded, enter your answer as “99999”.)