Question

`int_0^3 [x]dx` = ______, where [x] is greatest integer function.

Options

• 3

• 0

• 2

• 1

Answer 1

`int_0^3 [x]dx` = 3, where [x] is greatest integer function.

Explanation:

`int_0^3 [x]dx = int_0^1 0  dx + int_1^2 1  dx + int_2^3 2  dx`

= `[x]_1^2 + 2[x]_2^3`

= (2 – 1) + 2(3 – 2)

= 3