The area (in square units) bounded by the curve \(y = |x - 2|\) between \(x = 0\), \(y = 0\) and \(x = 5\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6.5
The graph of \(y = |x - 2|\) is a V with its vertex at (2, 0):
\( \displaystyle y = \begin{cases}2 - x, & x \lt 2\\x - 2, & x \ge 2\end{cases} \)
The region from x = 0 to x = 5 is made of two triangles.
From x = 0 to x = 2: base 2, height y(0) = 2.
\( \displaystyle \text{Area} = \frac{1}{2}\times 2\times 2 = 2 \)
From x = 2 to x = 5: base 3, height y(5) = 3.
\( \displaystyle \text{Area} = \frac{1}{2}\times 3\times 3 = 4.5 \)
Total area = 2 + 4.5 = 6.5 square units.