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gotmilk04
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Homework Statement
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
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]