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Help with Proof on Integration 
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#1
Nov1512, 12:28 PM

P: 2

I was assigned this problem in class. My instructor said it was a very popular theorem, but I cannot find it in my book or online. I am clueless on what to do. I would appreciate the help.
Let f(x) be bounded and integrable on [a, b]. Assume that g(x) differs from f(x) on only finitely many points in the domain. Show that g(x) is integrable. Moreover, show that ∫f(x)dx = ∫g(x)dx (Both integrals are from b to a). 


#2
Nov1512, 01:01 PM

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hi tomhawk24! welcome to pf!
start with the definition … which definition of integral (or integrable) are you using? 


#3
Nov1512, 01:36 PM

P: 2

Well we are working mainly on the Fundamental Theorem of Calculus right now.



#4
Nov1512, 01:43 PM

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P: 26,148

Help with Proof on Integration
ok, we'll start with that, then …
what does the fundamental theorem of calculus say? 


#5
Nov1612, 09:22 AM

P: 295

Starting from the area interpretation of the integral, answer this question: If I take finitely many points out of the graph of a curve f(x) and place them at some other ycoordinate, would the function still be integrable? What would be its integral?
Tip: Does a point have dimensions, or does a line have width? What is the area of a rectangle? 


#6
Nov1612, 09:30 AM

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P: 2,264

First show
∫(f(x)g(x))dx =0 then use linearity 


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