Find the area.

Calculus Level 4

The area of the region bounded by [ x ] 2 = [ y ] 2 [x]^{2}=[y]^{2} , if x € [ 1 , 5 ] x€[1,5] where [.] denotes the greatest integer function , is


The answer is 8.

Arghyanil Dey by Arghyanil Dey , 26, India

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1 solution

use graphs..

i am just giving one case..

Let x belongs to [1,2)

so, [x] =1

so, [y]= 1 and -1 hence, y belongs to [1,2) and [-1,0)

hence these are two square boxes of area 1 unit.

And there will be 4 such cases namely [1,2) , [2,3) , [3,4), [4,5)

And each time 2 square boxes of unit area will be formed

so total area = 2*4 = 8

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Fine!!!

Arghyanil Dey - 7 years, 1 month ago

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