The value of - 2 2 ( 1[x] + 4 ) dx, where [ ] denotes the greatest integer function, is
- 160(21 - 1)
- 160( - 7)
- 760( - 3)
- 760(3 - 1)
Answer
(4) 760(3 - 1)
Solution
2 1.57, split at x = -1, 0, 1:
I = - /2-1 dx-2 + 4 + -10 dx-1 + 4 + 01 dx0 + 4 + 1 /2 dx1 + 4
= 12 ( 2 - 1 ) + 13 + 14 + 15 ( 2 - 1 )
= 710 ( 2 - 1 ) + 712
= 7 20 - 710 + 712
= 21 60 - 760 = 760(3 - 1)
Answer: (4)