Find the area bounded by the curve $y = |x - 1|$ and $y = 1$, using integration.

$1$ sq unit

The correct answer is Option (2) → $1$ sq unit

We have, $y = |x - 1|$

$y = x - 1$ if $x - 1 \geq 0$

$y = -x + 1$ if $x - 1 < 0$

Required area = Area of shaded region

$A = \int\limits_{0}^{2} y \, dx$

$= \int\limits_{0}^{1} (1 - x) \, dx + \int\limits_{1}^{2} (x - 1) \, dx$

$= \left[ x - \frac{x^2}{2} \right]_{0}^{1} + \left[ \frac{x^2}{2} - x \right]_{1}^{2}$

$= (1 - \frac{1}{2}) - (0 - \frac{0}{2}) + (\frac{4}{2} - 2) - (\frac{1}{2} - 1)$

$= \frac{1}{2} + \frac{1}{2} = \mathbf{1 \text{ sq. unit}}$