Comprehension

Consider the following for the two (02) items that follow:
Let f(x) = [x2] where [.] is the greatest integer function.

What   equal to?

This question was previously asked in
NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. 1

Answer (Detailed Solution Below)

Option 2 :
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Detailed Solution

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Calculation:

Given,

The function is , where is the greatest integer function.

We are tasked with finding:

Decomposing the integral based on the function:

For \, x2 lies between and 1, so . Therefore,

For, x2  lies between 1 and 2, so Therefore,

For , x2  lies between 2 and 3, so . Therefore,

Summing up all the results:

= .

Hence, the correct answer is Option 2. 

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