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 four significant digits.)

Question

Enclosed by y = e^x, y = 2x + 1, x = −2, and x = 1

Answer 1

look at the graph first.

http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5Ex%2C+y+%3D+2x%2B1%2C+-2+to+1

I is obvious that y = e^x and y = 2x+1 intersect at the y-axis at (0,1). there is another intersection but it beyond x = 1, so of no concern to us
So area
= ∫ (e^x - 2x - 1)dx from -2 to 0 + ∫(2x + 1 - e^x) dx from 0 to 1

the integration and evaluation are straightforward