An integral my Ti-89 refused to do

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    Integral Ti-89
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Discussion Overview

The discussion revolves around the indefinite integral of sin(x)/(1+x^2)dx, with a specific focus on evaluating the definite integral over the interval from -1 to 1. Participants explore various approaches to solving the integral and clarify their understanding of the problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants question whether the integral can be expressed in terms of elementary functions.
  • One participant suggests graphing the function to gain insight into the integral's behavior over the specified interval.
  • Another participant proposes breaking the integral into two parts, from -1 to 0 and from 0 to 1, and applying a change of variable.
  • There is a discussion about the symmetry of the function, with one participant noting that the integral evaluates to zero due to the cancellation of areas under the curve.
  • Participants express varying levels of understanding regarding the mathematical manipulations involved in solving the integral.

Areas of Agreement / Disagreement

Participants generally agree on the symmetry of the function leading to a zero integral over the interval, but there is no consensus on the method to arrive at this conclusion or the nature of the indefinite integral.

Contextual Notes

Some participants express confusion about the steps involved in changing variables and the overall approach to solving the integral, indicating a need for clearer explanations of the mathematical processes.

Who May Find This Useful

This discussion may be useful for students learning about definite integrals, symmetry in functions, and variable substitution techniques in calculus.

kidwithshirt
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Homework Statement



Indefinite integral of sin(x)/(1+x^2)dx


Homework Equations





The Attempt at a Solution

 
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What reason do you have to believe that has an indefinite integral that can be written in terms of elementary functions?
 
HallsofIvy said:
What reason do you have to believe that has an indefinite integral that can be written in terms of elementary functions?

i m sorry i don't really comprehend what you are trying to say here.

By the way my mistake on my behalf, it is the integral between the interval of -1 and 1

I don't know how to get started
 
This question has a very simple answer. Try graphing the function from -1 to 1 and you might see it.
 
i realized that in the first place, but is there a mathematical manipulation that could get the result?
 
Break the integral up into integrals from -1 to 0 and from 0 to 1. In the first, make a change of variable, x -> -x.
 
Avodyne said:
Break the integral up into integrals from -1 to 0 and from 0 to 1. In the first, make a change of variable, x -> -x.

i don't understand what you are saying >.<

i started calc this year.

Could you show me your steps really quick
 
First tell me what the value of the integral is, and give your best explanation.
 
according to the graph it's 0 because the line is reflected on the origin so the two regions canceled each other out.
 
  • #10
Yes, exactly. So the integral over the left half (from -1 to 0) must equal minus the integral over the right half (from 0 to 1).

Do you know how to change variables in an integral? You want to change the variable in the left-half integral from x to -x, and then show that the result is equal to minus the right-half integral.
 

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