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Find the value of int(0)^(4)[x]dx, where...

Find the value of `int_(0)^(4)[x]dx`, where `[.]` represents the gretest integer function.

Text Solution

Verified by Experts

The correct Answer is:
6
Graph of `y=[x]` for `0ltxlt4` is as shown in the following figure.

From the graph `int_(0)^(4)[x]dx=0` (for `0ltxlt1)`
`+(1xx1)` (for `1ltxlt2`)
`+(1xx2)` (for `2ltxlt3`)
`+(1xx3)` (for `3ltxlt4`)
`=0+1+2+3`
`=6`
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