Improper Integrals / Antiderivatives.

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Homework Help Overview

The discussion revolves around evaluating improper integrals, specifically focusing on the antiderivatives involved in the process. The subject area is calculus, particularly the concepts of integration and improper integrals.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses difficulty with finding antiderivatives, especially in fractional forms, and seeks clarification on the process. Some participants inquire about the derivative of the natural logarithm and its relationship to integration, while others attempt to clarify the integration of specific functions.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the antiderivative concept and questioning the original poster's understanding. There is an exchange of ideas regarding the relationship between differentiation and integration, but no consensus has been reached yet.

Contextual Notes

The original poster's confusion appears to stem from the transition between different forms of functions in the context of improper integrals, indicating a potential gap in understanding the foundational concepts of integration.

mortokr
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Homework Statement


Evaluate each improper integral whenever it is convergent.

1. S 1-infinity 4 / x

2. S 4 - infinity 2/x^3/2

Homework Equations





The Attempt at a Solution



I'm having trouble with antiderivatives. I understand how to do them when the problem is like x^4 + x^2 + 3 or something but anytime they're in like a fraction form I get lost and the first step in improper integrals is finding the antiderivative.
 
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well firstly do you know what is d/dx (lnx) gives?

Secondly 1/an = a-n
 
ln x = 1/x right?

So, 4/x would just be x2?
 
mortokr said:
d/dx(lnx) = 1/x right?


mortokr said:
So, 4/x would just be x2?

No. If you differentiate lnx with respect to x to get 1/x, and integration is the reverse of differentiation, then the integral of 1/x with respect to x gives what?
 

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