An integral my Ti-89 refused to do

[kidwithshirt]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

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

 

[kidwithshirt]

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

 

[Avodyne]

This question has a very simple answer. Try graphing the function from -1 to 1 and you might see it.

 

[kidwithshirt]

i realized that in the first place, but is there a mathematical manipulation that could get the result?

 

[Avodyne]

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.

 

[kidwithshirt]

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

 

[Avodyne]

First tell me what the value of the integral is, and give your best explanation.

 

[kidwithshirt]

according to the graph it's 0 because the line is reflected on the origin so the two regions canceled each other out.

 

[Avodyne]

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.