Given curve: y = loge (x e)
To find: The area enclosed between the curve and the coordinate axes.

To find the area enclosed by the curve and the coordinate axes, we need to determine the limits of integration and the integrand.

Step 1: Determine the limits of integration
To determine the limits of integration, we need to find the x-values where the curve intersects the coordinate axes.

When y = 0, we have:
0 = loge (x e)

Using the property of logarithms, we can rewrite the equation as:
1 = x e

Solving for x, we get:
x = e - 1

So, the lower limit of integration is e - 1.

When x = 0, we have:
y = loge (0 e)
y = loge (0)

The natural logarithm of zero is undefined, so the curve does not intersect the y-axis. Therefore, the upper limit of integration is 0.

Step 2: Determine the integrand
The area between the curve and the x-axis can be found by integrating the absolute value of the curve's equation. Since the curve is always positive, we can simply integrate the curve's equation.

The integrand is:
f(x) = loge (x e)

Step 3: Calculate the area
The area enclosed between the curve and the coordinate axes can be found using the definite integral:
A = ∫[a,b] f(x) dx

Substituting the limits of integration, we have:
A = ∫[e - 1, 0] loge (x e) dx

To evaluate the integral, we can use integration by parts or use a calculator. After evaluating the integral, we find that the area is equal to 1.

Therefore, the correct answer is option 'A': 1.