$\int\limits_0^2(|x|+|x-2|)dx =$

4

The correct answer is Option (2) → 4

Integral:

$\displaystyle \int_{0}^{2} \left(|x| + |x-2|\right)\,dx$

On $[0,2]$:

$|x| = x$ (since $x\ge 0$)

$|x-2| = 2 - x$ (since $x-2\le 0$)

So the integrand becomes:

$x + (2 - x) = 2$

Integral:

$\displaystyle \int_{0}^{2} 2\,dx = 2[x]_{0}^{2} = 2(2 - 0) = 4$

Answer = 4