Question

Find the area enclosed in the first quadrant represented by the function [x] + y = 1 where [x] is the greatest integer less than or equal to x.

• A. 1
• B. 8
• C. Infinity
• D. 2

Answer 1

The correct option is A 1

For x = 0 to x = 1 $\Rightarrow$ y = 1

When x = 0.9999999, [x] = 0, thus y = 1

Thus the area will be very close to, but slightly less than 1

Thus, the area enclosed in the first quadrant can be represented as follows

Required area = 1$\times$1= 1