Strange integral of heaviside step function

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The integral of the Heaviside step function, expressed as ∫Θ(f - f(t))dt, is discussed in the context of solid state physics, specifically in Ashcroft and Mermin's book. The integral is evaluated from 0 to infinity, resulting in the expression t_max - t_min. Participants are seeking clarification on the meaning and implications of this integral. Additionally, there is a request for a visual reference from the book to better understand the context of the integral. Understanding this integral is crucial for grasping concepts in solid state physics.
cytochrome
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I ran across this integral while reading Ashcroft and Mermin's solid state physics book...

∫Θ(f - f(t) )dt = t_max - t_min

Where Θ is the heaviside step function and the integral runs from 0 to infinity.

Does anyone have any idea how this integral makes sense?
 
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cytochrome said:
I ran across this integral while reading Ashcroft and Mermin's solid state physics book...

∫Θ(f - f(t) )dt = t_max - t_min

Where Θ is the heaviside step function and the integral runs from 0 to infinity.

Does anyone have any idea how this integral makes sense?
Can you post a picture of the page that shows this integral?
 

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