For the function f(x)= cases 2x+1, & 0 x<3, 7, & 3 x 5

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

Problem

For the function

f(x)=\begin{cases}2x+1, & 0\le x<3,\\7, & 3\le x\le 5,\end{cases}

answer the following. (a) Part 1: (i) Identify the sub-intervals on which

f(x)

is defined by different expressions. (b) Part 2: (ii) Write an integral expression for the average value of

f(x)

on the interval

[0,5]

. (c) Part 3: (iii) Evaluate the integral(s) obtained in (ii) and hence find the average value of

f(x)

[0,5]

. Express your answer in simplest form.