Help Solving Integral Limit: x to 1

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Discussion Overview

The discussion revolves around evaluating the limit of an integral as x approaches infinity, specifically the expression involving the integral of cos(t) divided by t squared from x to 1. The focus is on the mathematical reasoning and techniques involved in solving this limit.

Discussion Character

  • Mathematical reasoning, Homework-related

Main Points Raised

  • One participant presents the limit expression involving the integral of cos(t)/t² from x to 1 as x approaches infinity.
  • Another participant seeks clarification on the expression, suggesting a more formal notation for the limit and integral.
  • A subsequent participant confirms the integral's limits but notes that there is an additional x before the integral, indicating a potential misunderstanding or complexity in the expression.
  • Another participant provides a hint regarding the bounds of t in the integral, suggesting that t is constrained between x and 1, which affects the behavior of the integrand.
  • One participant recommends using integration by parts and emphasizes the importance of tracking signs throughout the process.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the exact formulation of the limit or the method of evaluation, indicating that multiple interpretations and approaches are present in the discussion.

Contextual Notes

The discussion includes assumptions about the behavior of the integral as x approaches infinity and the implications of the bounds on t. There may be unresolved mathematical steps related to the integration technique suggested.

Who May Find This Useful

This discussion may be useful for students or individuals interested in advanced calculus, specifically those dealing with limits of integrals and integration techniques.

erogol
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lim x [tex]\int cost / t^2[/tex] (integral x to 1) x goes infitine
 
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Did you mean:
[tex]\lim_{x \to \infty} \int_x^1 \frac{\cos t}{t^2} \, dt[/tex]
?
 
yes:) but there is a x before the integral
 
Hint: t is in [x,1] i.e 1/t^2 is in [1,1/x^2].
 
integrate via parts and keep track of your signs
 

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