Consider the function defined on the closed interval

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the function

g(x)=e^{ax}+2

defined on the closed interval

[\ln 2,\,\ln 8]

, where

a

is a non-zero real constant. The average value of

g

over this interval must equal

9

. Solve for the constant

a

. Clearly justify each step of your solution.