Draw a rough sketch of the curve $y = 1 + |x + 1|$, $x = -3$, $x = 3$, $y = 0$ and find the area of the region bounded by them using integration.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $16$ sq units
Required area $= \int\limits_{-3}^{-1} -x \, dx + \int\limits_{-1}^{3} (x + 2) \, dx$
$= \left[ \frac{-x^2}{2} \right]_{-3}^{-1} + \left[ \frac{x^2}{2} + 2x \right]_{-1}^{3}$
$= \frac{-1}{2} (1 - 9) + \left[ \left( \frac{9}{2} + 6 \right) - \left( \frac{1}{2} - 2 \right) \right]$
$= 4 + 12 = \mathbf{16 \text{ sq. units.}}$