(8)

To solve this, we start by evaluating the integral:

The greatest integer function [ ] returns the largest integer less than or equal to the input value. Here's how we can approach the problem:

Determine the function inside the integral:

Identifying the intervals:
When , which simplifies to , we have .

When , simplifying gives , and thus .

When , which holds for , thus from to .

Evaluate the integral on these intervals:

Combine these results:

Thus, we are given that:

This implies that:

Therefore, .

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