Let be continuous on and let g(x)=A ,f(Bx+C)+D

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

Problem

Let

f

be continuous on

\mathbb R

and let

g(x)=A\,f(Bx+C)+D,

where

A,B\neq0,\;C,\,D

are constants and

p<q

. (i) Derive an expression for the average value of

g

on the interval

[p,q]

in terms of

A,\,B,\,D

and the average value of

f

over a suitable interval to be determined. (ii) From the expression obtained in part (i), explain separately how varying

A

and how varying

D

influence the average value of

g