Question

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. (Round your answer to three decimal places.)
Between y = e^x and y = x for x in [0, 1]

Answer 1

y=e^x is always greater than y=x, so the area is:
\[Area\ under\ e^x - Area\ under\ x \\ \int\limits_{0}^{1}e^x\ dx - \int\limits_{0}^{1} x\ dx\]