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 can follow these steps:

### Step 1: Understand the curve and the boundaries
The curve \(y^2 = x\) represents a parabola that opens to the right. The lines \(x = 1\) and \(x = 4\) are vertical lines that will serve as the left and right boundaries of the area we want to find. The x-axis will be the lower boundary.

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