Question

(a) Compute the area of the bounded region enclosed by the curve y = e^x, the line y = 12, and the y-axis.
(b) How does this area compare with the value of the integral ∫1-12(ln x dx)? Explain your answer. (A picture may be helpful.)

Answer 1

intersection of y = 12 and y = e^x
e^x = 12
x = ln 12

area = ?(12 - e^x)dx from 0 to ln12
= [12x - e^x] from 0 to ln12
= 12ln12 - e^(ln12) - (0 - e^0)
= 12ln12 - 12 - 0 + 1
= 12ln12 - 11

http://www.wolframalpha.com/input/?i=area+between+y+%3D+e%5Ex,++y+%3D+12+from+0+to+ln12