Question

Consider the curve 𝑓(𝑥) = ln(𝑒𝑥) on the interval [1, 2]. Note: 𝑓(𝑥) is positive on the given 𝑥interval.

a) Find the exact area under the curve on the given interval.

b) Is the curve increasing or decreasing on the given interval?

c) Use Riemann sums with 𝑛 = 2 subintervals to find both an upper bound and lower bound to the exact area found in part (a). No simplification necessary. [Hint: use part b) to determine how to find an upper and lower bound]