Help with Proof on Integration


by tomhawk24
Tags: integration, proof
tomhawk24
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#1
Nov15-12, 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).
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tiny-tim
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#2
Nov15-12, 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?
tomhawk24
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#3
Nov15-12, 01:36 PM
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Well we are working mainly on the Fundamental Theorem of Calculus right now.

tiny-tim
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Nov15-12, 01:43 PM
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Help with Proof on Integration


ok, we'll start with that, then
what does the fundamental theorem of calculus say?
Millennial
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#5
Nov16-12, 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 y-coordinate, 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?
lurflurf
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#6
Nov16-12, 09:30 AM
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First show
∫(f(x)-g(x))dx =0
then use linearity


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