Define [x] as the greatest integer less than or equal to x, for each x(-,). If y=[x], find the area under y for x[1,4].

GATE 2020 MT – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

Define $[x]$ as the greatest integer less than or equal to x, for each $x\in(-\infty,\infty)$. If $y=[x]$, find the area under y for $x\in[1,4]$.

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Correct answer: (D) 6

Explanation

The floor function is 1 on [1,2), 2 on [2,3), and 3 on [3,4). Each interval has width 1. The integral is therefore $1+2+3=\mathbf6$. The isolated value at x=4 contributes no area. **Answer: D.**

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