Area of the region bounded by the curve y = ex and lines x = 0 and y = e is:

The area of the region bounded by the curve y = ex and the lines x = 0 and y = e can be calculated using integration. The area can be expressed as the integral of the difference between the upper curve (y = e) and the lower curve (y = ex) with respect to y, from y = 1 to y = e. The x limits are from x=0 to x = ln y. This can be represented as:
Area = ∫1e ln y dy
Alternatively, we can integrate with respect to x, where the area is given by:
Area = e - ∫01 ex dx
Evaluating the integral:
Area = e - [ex]01 = e - (e1 - e0) = e - (e - 1) = 1
However, the question mentions several integral expressions, and the area can be correctly calculated as:
Area = e - ∫01 ex dx = e - [ex]01 = e - (e - 1) = 1
Therefore, the correct expression representing the area is e - ∫01 ex dx