The function is continuous on the interval

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

The function

f(x)=3x+2

is continuous on the interval

[1,b]

, where

b>1

. Its average value on this interval is

11

. (i) Evaluate

\displaystyle \int_1^b f(x)\,dx

and simplify your result. (ii) Using the result of part (i), form an equation in

b

corresponding to the given average value. (iii) Solve the equation obtained in part (ii) to determine the value of

b