For the function

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

Problem

For the function

p(x)=4x-1

, the average value on the interval

[0,b]

equals

7

, where

b>0

. (i) Evaluate

\displaystyle \int_0^b p(x)\,dx

. (ii) Form an equation in

b

corresponding to the given average value and hence determine the value of

b