GATE EE 2018 Set 1 — Question 28
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Engineering Mathematics → Calculus → Definite & Improper Integrals
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Question
Let be a real-valued function of a real variable defined as , where denotes the largest integer less than or equal to . The value of is _______ (up to 2 decimal places).
Correct answer
0.49 to 0.51
Solution
The function is the fractional part function, which is periodic with period . A property of periodic functions is that the integral over any interval of length equal to the period is constant: In this case, and . Therefore:In the interval , the greatest integer function . Thus, .
Evaluating the integral:The value of the integral is 0.5.
Evaluating the integral:The value of the integral is 0.5.
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