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 [1, 2]
Between y = e^x and y = x for x in [1, 2]
Answers
as you can see from the graph, they do not intersect, so we simple take the integral from 1 to 2
area = ∫ e^x - x dx from 1 to 2
= [e^x - x^2/2] from 1 to 2
= e^2 - 2 - (e^1 - 1/2)
= e^2 - e - 3/2
area = ∫ e^x - x dx from 1 to 2
= [e^x - x^2/2] from 1 to 2
= e^2 - 2 - (e^1 - 1/2)
= e^2 - e - 3/2