Question

The area of the region bounded by the lines \(2x-y+1 = 0, y = -1, y = 3\) and the y-axis is _____

• A. \(2\)
• B. \(5\)
• C. \(3\)
• D. \(4\)

Hint:

Integrate \(|x|\) with respect to \(y\) where \(x=\frac{y-1}{2}\).

Answer 1

The Correct Option is A

Step 1: Use triangles
The region is two right triangles. Left: vertices $(0,1)$, $(0,-1)$, $(-1,-1)$ with legs 2 and 1, area 1.

Step 2: Right triangle
Vertices $(0,1)$, $(0,3)$, $(1,3)$ with legs 2 and 1, area 1. Total 2, option (A).

Final Answer:
The total area is 2 sq. units, option (A). \[ \boxed{2} \]