Question

The area of the region bounded by the curves \(y = |x-4|\), \(x = 3\) and \(x = 5\), and the X-axis is

• A. \(5\) sq. units
• B. \(3\) sq. units
• C. \(6\) sq. units
• D. \(1\) sq. unit

Hint:

The graph is a V shape with vertex at (4, 0), so the area is two small triangles.

Answer 1

The Correct Option is D

Step 1: Triangles
Each part is a right triangle with base 1 (from $x = 3$ to 4, and 4 to 5) and height 1.

Step 2: Area of each
$\frac12 \times 1 \times 1 = \frac12$.

Step 3: Total
$\frac12 + \frac12 = 1$. Option (D).

Final Answer:
Option (D). \[ \boxed{1 \text{ sq. unit}} \]