(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define f as: f(x)= 2 if 0[tex]\leq[/tex]x<1

f(1)=0

f(x)= -1 if 1<x<2

f(2)= 3

f(x)=0 if 2<x<3

f(3)=1

Prove f is integrable using six subintervals and find the value of [tex]\int[/tex]f(x) dx

3. The attempt at a solution

Let P={0, 1-h, 1+h, 2-h, 2+h, 3-h, 3} where 0<h<1/2

I just need help proving [tex]\int[/tex]f(x) dx=1.

I can prove I[tex]\geq[/tex]1, but I'm having trouble proving J<1+[tex]\epsilon[/tex]

I have S[tex]_{P}[/tex]=2(1-h)+2(2h)+(-1)(1-2h)+3(2h)+0(1-2h)+h= 2+9h

but now I don't know how to get that to less than 1+[tex]\epsilon[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Prove f is integrable using six subintervals and evaluate.

**Physics Forums | Science Articles, Homework Help, Discussion**