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Answer:
.} - Fractional part of x.
[.] - Greatest integer function.
As integration can be broken into parts, where as integration of x−−√ is easy , so lets look for the integration for [ x−−√ ].
We just need to check where this greater integer function is discontinous beause those will be the points where we have to break the integration again.
Break 1: When x varies from 0 to 1 [ x−−√ ] value will be 0.
Break 2: When x varies from 1 to 4 [ x−−√ ] value will be 1.
Break 3: When x varies from 4 to 9 [ x−−√ ] value will be 2.
So the integration becomes:
∫90x−−√dx - ( ∫100dx + ∫411dx + ∫942dx )
Rest I leave it for you.
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