Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.

Question

enclosed by y = ex, y = 5, and the y-axis

Answer 1

So, having drawn the graphs, it should be clear that the area can be considered as a collection of vertical strips of width dx, making it
A = ∫[0,ln5] (5-e^x) dx = 5ln5 - 4

or, as a set of horizontal strips of width dy,
A = ∫[1,5] lny dy = 5ln5 - 4