Improper Integrals: Struggling to Understand Convergence

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Homework Help Overview

The discussion revolves around the concept of improper integrals, specifically focusing on the conditions that classify an integral as improper. The original poster expresses confusion regarding the classification of a particular integral and its convergence based on a provided graph.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the reasoning behind the integral being classified as improper, particularly in relation to the graph they provided. Some participants clarify the definition of improper integrals, noting that they can involve infinite bounds or discontinuities.

Discussion Status

The discussion is ongoing, with participants providing definitions and clarifications about improper integrals. There is an exploration of the original poster's misunderstanding regarding the infinite interval of integration, but no consensus has been reached on the specific integral in question.

Contextual Notes

The original poster references a solution manual that states the integral has an infinite interval of integration, which they find confusing in light of their graph. This indicates a potential discrepancy between their understanding and the material they are studying.

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Homework Statement



I don't understand why the following intergral is improper
http://img413.imageshack.us/img413/1667/38410700.jpg

I have a graph for the function.
http://img413.imageshack.us/img413/2424/photoxxs.jpg

According to this graph, the function should converge in [-∞,0)
However, my solution manual says that the function has an infinite interval of integration.

Could anyone tell me what I am mistaken?

Thank you for reading.
 
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Improper integrals may either converge or diverge, that is, have a finite value or not. An improper integral is an integral involving an infinity in either or both bounds, or one whose integrand is discontinuous over the interval.
 
Oh I should have studied more.

Thank you. :)
 
"Infinite interval of integration" simply means that you are integrating from -infinity to 0, an infinite length.
 

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