Solving Integrals with Limits: A Step by Step Guide

  • Thread starter Thread starter rey242
  • Start date Start date
  • Tags Tags
    Integral Limit
Click For Summary

Homework Help Overview

The discussion revolves around evaluating an integral with limits as a variable approaches infinity, specifically involving the function cos(e^x). Participants are exploring the implications of changing integration variables and the behavior of the function within the limits of integration.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the use of substitution in integrals and the implications of variable limits. Questions arise regarding the correct interpretation of limits and the behavior of the function being integrated as the variable approaches infinity.

Discussion Status

The conversation is ongoing, with participants providing insights into the nature of the integral and the bounded behavior of the cosine function. There is a mix of interpretations regarding the limits and the approach to evaluating the integral, with no clear consensus yet.

Contextual Notes

Participants are navigating the nuances of integration limits and the behavior of the integrand as the variable approaches infinity, indicating potential confusion about the setup of the problem.

rey242
Messages
40
Reaction score
0
Limit with integrel

Homework Statement


equationrender.png


Homework Equations





The Attempt at a Solution


I tried to take
x=ln(u)
dx=du/u
and solve the integral but I keep getting stuck at the int(cos(u)/u.)
Can anyone help me out here?
 
Physics news on Phys.org


You can't take the limit x->infinity. x is a dummy integration variable. You must mean n->infinity. Right?
 


I meant N.
Sorry, its a force of habit.
 


Ok, then as n->infinity then 1/n -> 0. You don't actually have to do the integral to know what the limit is, because cos(e^x) is bounded. What's the limit of the integral of a bounded function between 0 and 1/n as n->infinity?
 


so the integral would be zero as n approaches inf. since the limits of integration go from zero to zero, right?
 


No, it's not just the limits of integration, you have to think about how the function you are integrating behaves. -1<=cos(e^x)<=1. Agree? So what limits can you make for the integral from 0 to 1/n of cos(e^x)? What happens as n->infinity?
 


I'd try the MVT.
 

Similar threads

  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K