retagged by
1,018 views
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. $1$
  2. $3$
  3. $4$
  4. $6$
retagged by
Migrated from GO Mechanical 2 years ago by Arjun

1 Answer

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 $(D).$

edited by
Answer:

Related questions

5 votes
5 votes
2 answers
1
go_editor asked Feb 19, 2020
1,029 views
Select the graph that schematically represents BOTH $y=x^{m}\:\text{and}\:y=x^{1/m}$ properly in the interval $0\leq x \leq 1$, for integer values of $m,$ where $m 1.$
2 votes
2 votes
1 answer
3
0 votes
0 votes
1 answer
4
go_editor asked Feb 19, 2020
560 views
He is known for his unscrupulous ways. He always sheds ________tears to deceive people.fox’scrocodile’scrocodilefox