Help Solving Integral Limit: x to 1

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SUMMARY

The discussion centers on evaluating the limit of the integral \(\lim_{x \to \infty} \int_x^1 \frac{\cos t}{t^2} \, dt\). Participants clarify that the integral is defined from \(x\) to \(1\) and suggest using integration by parts while carefully tracking the signs. The key takeaway is that as \(x\) approaches infinity, the behavior of the integral is influenced by the bounds and the function \(\frac{\cos t}{t^2}\).

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with definite integrals
  • Knowledge of integration by parts technique
  • Basic trigonometric functions and their properties
NEXT STEPS
  • Study the method of integration by parts in detail
  • Explore the properties of improper integrals
  • Investigate the behavior of \(\cos t\) as \(t\) approaches infinity
  • Learn about convergence criteria for integrals
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on calculus and analysis, will benefit from this discussion. It is also useful for educators looking to enhance their understanding of integral limits and integration techniques.

erogol
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lim x \int cost / t^2 (integral x to 1) x goes infitine
 
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Did you mean:
\lim_{x \to \infty} \int_x^1 \frac{\cos t}{t^2} \, dt
?
 
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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