Question

Evaluate:

`int_0^sqrt(2)[x^2]dx`

Answer 1

`int_0^sqrt(2)[x^2]dx`

We know greatest integer function is discontinuous when x is an integer.

∴ `int_0^sqrt(2)[x^2]dx = int_0^1 0  dx + int_1^sqrt(2) 1  dx`

= `x|_1^sqrt(2)`

= `sqrt(2) - 1`