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int(0)^(x) dx = "…….", where [x] is grea...

`int_(0)^(x) dx = "……."`, where [x] is greatest integer function.

A

3

B

0

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I = int_(0)^(3) [x] dx`
`= int_(0)^(1) 0 dx + int_(1)^(2) 1dx + int_(2)^(3) 2dx`
`= [x]_(1)^(2) + 2[x]_(2)^(3)`
` = (2-1) + 2(3-2) = 1 + 2 = 3`
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