Question
Question: The value of ![](https://cdn.pureessence.tech/canvas_411.png?top_left_x=300&top_left_y=1116&width=30...
The value of dx, where [x] is the greatest integer less than or equal to x is –
A
2
B
8/3
C
4
D
None of these
Answer
None of these
Explanation
Solution
For x Ī [0, 2], x2 + 1 Ī [1, 5],
we must break [0, 2] = [0, 1] Ē [1, 2 ]
=[0, 1] Č [1, 2 ] Č[ 2 , 3 ] Č [ 3 , 2].
Hence dx
= dx + ∫12x[x2+1] dx + ∫23x[x2+1] dx + ∫32x[x2+1] dx
= 31[23/2 – 1] + 51 35/2.