If A denotes the area between the curve 2{y} = [x] + 1 for 0 ≤ y 2 - x ≤ 0, then A is le

Question

If A denotes the area between the curve 2{y} = [x] + 1 for 0 &#8804; y 2 - x &#8804; 0, then A is less than or equal to (where {.} and [.] are the fractional part and greatest integer functions respectively) -

Accepted Answer

2{y} = [x] + 1 ....(1)&#8757; 0 &#8804; y < 1 &#8658; {y} = y&#8756; (1) &#8658; 2y = [x] + 10 &#8804; [x] + 1 < 2- 1 &#8804; [x] < 1but [x] is an integer&#8658; [x] = - 1 &#8658; -1 &#8804; x < 0[x] = 0 &#8658; 0 &#8804; x < 1when x &#8712; [-1, 0) &#8658; y = 0when x &#8712; [0, 1) &#8658; y = &#8756; Area =

Question

Options

Solution

More Set, Relation and Function Questions