Question
Question: Area of region bounded by [x]<sup>2</sup> = [y]<sup>2</sup> if x Î [1, 5]where [.] represents the gr...
Area of region bounded by [x]2 = [y]2 if x Î [1, 5]where [.] represents the greatest integer function, is -
A
10 sq. units
B
8 sq. units
C
6 sq. units
D
5 sq. units
Answer
8 sq. units
Explanation
Solution
If 1 £ x < 2 Ž [x] = 1 Ž [y] = ± 1
y Ī [–1, 0) Č [1, 2)
If 2 £ x < 3 Ž [x] = 2 Ž [y] = ± 2
y Ī [–2, – 1) Č [2, 3)
If 3 £ x < 4 Ž [x] = 3 Ž [y] = ± 3
y Ī [–3, –2) Č [3, 4)
If 4 £ x < 5 Ž [x] = 4 Ž [y] = ± 4
y Ī [– 4, – 3), Č [4, 5)
from figure required area consist of eight squares each of area unity Required area = 8 sq. unit