Question

The value of the integral `int_0^sqrt(2)([sqrt(2 - x^2)] + 2x)dx` (where [.] denotes greatest integer function) is ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

The value of the integral `int_0^sqrt(2)([sqrt(2 - x^2)] + 2x)dx` (where [.] denotes greatest integer function) is 3.00.

Explanation:

= `int_0^1[sqrt(2 - x^2)]dx +  int_1^sqrt(2)[sqrt(2 - x^2)]dx + int_0^sqrt(2)2xdx`

= `int_0^1(1)dx + int_1^sqrt(2)(0)dx + (x^2)_0^sqrt(2)`

= 1 + 0 + 2

= 3