Find the area of the region bounded by the curve `y^2= x`and the lines `x = 1, x = 4`and the x-axis.

Explanation

To find the area of the region bounded by the curve \( y^2 = x \), the lines \( x = 1 \), \( x = 4 \), and the x-axis, we will follow these steps:

### Step 1: Understand the curve and the boundaries
The equation \( y^2 = x \) represents a parabola that opens to the right. The lines \( x = 1 \) and \( x = 4 \) are vertical lines that will define the limits of integration. The x-axis is the line \( y = 0 \).

### Step 2: Express \( y \) in terms of \( x \)
From the equation \( y^2 = x \), we can express \( y \) as:
\[
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