Question

`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.

Options

• `1/2 + π/6`

• `1 - sqrt(3)/2 + π/6`

• `-1/2 - π/6`

• `sqrt(3)/2 - 1 - π/6`

Answer 1

`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to `underlinebb(1 - sqrt(3)/2 + π/6)`.

Explanation:

In the interval `π/3` to `π/2`, [x] = 1

∴ I = `int_(π/3)^(π/2) x sin(π - x)dx`

= `int_(π/3)^(π/2) x sinx  dx`

= `[-x cos x + sin x]_(π/3)^(π/2)`

= `1 - sqrt(3)/2 + π/6`