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Define [x ] as the greatest integer less than or equal to x, for each x ∈(–∞, ∞). If y = [x], then area under y for x ∈[1, 4] is _______.
  • a)
    3
  • b)
    1
  • c)
    6
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Define [x ] as the greatest integer less than or equal to x, for each ...

Area = 1 × 1 + 1 × 2 + 1 × 3
= 1 + 2 + 3 = 6
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Define [x ] as the greatest integer less than or equal to x, for each ...
For any real number x, the greatest integer less than or equal to x, denoted [x], is the largest integer that is smaller than or equal to x. In other words, [x] is the floor function of x.

Mathematically, the greatest integer less than or equal to x can be defined as follows:
[x] = n, where n is an integer such that n ≤ x < n="" +="" />

For example:
[3.5] = 3
[-2.7] = -3
[0] = 0
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Define [x ] as the greatest integer less than or equal to x, for each x ∈(–∞, ∞). If y = [x], then area under y for x ∈[1, 4] is _______.a)3b)1c)6d)4Correct answer is option 'C'. Can you explain this answer?
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