4 votes 4 votes Define $[x]$ as the greatest integer less than or equal to $x$, for each $x\in \left (- \infty, \infty \right ).$ If $y = [x]$, then area under $y$ for $x\in \left [ 1,4 \right ]$ is _______. $1$ $3$ $4$ $6$ Quantitative Aptitude gateme-2020-set1 quantitative-aptitude functions + – go_editor asked Feb 19, 2020 • retagged Mar 6, 2021 by Lakshman Bhaiya go_editor 1.1k views answer comment Share Follow Migrated from GO Mechanical 3 years ago by Arjun See all 0 reply Please log in or register to add a comment.
Best answer 6 votes 6 votes The graph of $y = [x]$ for $x \in [1, 4]$. The required area $ = (1 \times 1) + (1 \times 2) + (1 \times 3) = 1 + 2 + 3 = 6 \;\text{unit}^{2}. \quad [\because $ Area of rectangle = Base $ \times $ Height $]$ So, the correct answer is $(D).$ Lakshman Bhaiya answered Feb 11, 2021 • edited Apr 8, 2021 by Lakshman Bhaiya Lakshman Bhaiya comment Share Follow See all 4 Comments See all 4 4 Comments reply Overflow04 commented Oct 31, 2022 reply Follow Share @Lakshman Patel RJIT @Kabir5454 can you elaborate this point with an example: [x] as the greatest integer less than or equal to x. 0 votes 0 votes Kabir5454 commented Oct 31, 2022 reply Follow Share y=f(x) , Then if x=6.6 then y=6 greatest integer less than or equal to 6.6 is 6. Similarly x=6.99999999 then also y=6. If x=6 then y=6 You can conclude from the graph as well. It form a steps like figure. 3 votes 3 votes Ray Tomlinson commented Sep 13, 2023 reply Follow Share great explanation bro, 0 votes 0 votes Ray Tomlinson commented Sep 13, 2023 reply Follow Share why answer is not 15, 0 votes 0 votes Please log in or register to add a comment.