What am I doing wrong with this simple integral?

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Homework Help Overview

The discussion revolves around the integration of the function x-2 over the interval from -1 to 1. Participants are exploring the implications of integrating a function that has an infinite discontinuity within the specified bounds.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are examining the validity of the integral and questioning the nature of the area under the curve, particularly in relation to the infinite discontinuity at x = 0. There are discussions about whether the integral can be computed and what the implications of the results mean.

Discussion Status

The conversation is ongoing, with participants expressing differing views on the nature of the integral and its result. Some guidance has been offered regarding the relationship between discontinuities in functions and their integrals, but no consensus has been reached on the validity of the original integration attempt.

Contextual Notes

There is a recognition of the complexities involved in integrating functions with infinite discontinuities, and participants are considering the implications of these mathematical properties on the problem at hand.

Physics_wiz
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I want to integrat x^-2 between -1 to 1. The answer shouldn't exist (should probably be something divided by 0) because the area is infinite between -1 to 1. But I integrate, and I get -x^-1 from -1 to 1. I then plug the bounds in and I get: [-(1)^-1] - [-(-1)^-1] which is -1 -1 or -2. What am I doing wrong?
 
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Physics_wiz said:
because the area is infinite between -1 to 1

Not true. You're right with your answer. One thing you will learn with integrals is that an infinite jump at any particular point in a function f(x) may correspond to a finite jump in its integral.
 
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vsage said:
Not true. You're right with your answer. One thing you will learn with integrals is that an infinite jump at any particular point in a function f(x) may correspond to a finite jump in its integral.

Why is the answer negative? I attached a picture of the graph, it still looks like it should be infinite to me.
 

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Ok my apologies. You were correct in your arithmetic, but your answer is complete garbage. As far as I know you cannnot integrate over that interval. There are however cases where a function "blows up" but has a finite integral, so you must be careful (the only case I know of however is the dirac delta function, whose integral is 1 over infinite limits)
 
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