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#1 2012-07-06 04:13:01
- William F
- Member
- Registered: 2012-07-03
- Posts: 16
Indefinite Integration
Hi all,
I'm having some trouble with this type of integration problem.
I break it into two parts first:
I solve each and get:
I end up with:
I've been using an online "Integrator" to check my work, and it keeps telling me the answer should be:
I'm not sure if my answer is just plain wrong, or needs to be manipulated somehow, or if the "Integrator" is throwing me off.
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#2 2012-07-06 04:24:35
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Indefinite Integration
Hi William F
Your answer and the answer from Online Integrator are the same.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
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#3 2012-07-06 04:24:35
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Indefinite Integration
Hi;
Let's go over what you have done:
you have left out the dx in yours. You must always have it.
Second line should look like this:
Answer should look like this
there is always an arbitrary constant of integration on that type of problem. The integrator will leave it out but you should not.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#4 2012-07-06 05:31:12
- William F
- Member
- Registered: 2012-07-03
- Posts: 16
Re: Indefinite Integration
bobbym, thank you for the tips. I realized after I posted that I'd ommitted the constant of integration and dx. I need to get used to writting everything out.
anonimnystefy, this isn't the first time I've been thrown by an answer in a different form. I guess my problem is in the algebra. What steps can be taken to show that:
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#5 2012-07-06 05:34:21
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Indefinite Integration
Hi;
There are some nice ways to prove to yourself that an identity exists.
Times both sides by 3.
Expand out:
Or you can plug in a few numbers. This is not 100% effective but will get the job done most of the time.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#6 2012-07-06 05:52:40
- William F
- Member
- Registered: 2012-07-03
- Posts: 16
Re: Indefinite Integration
That's exactly what I was looking for. Thanks again!
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#7 2012-07-06 05:56:12
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Indefinite Integration
Hi William F;
You are welcome.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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