In the answer, there is no -1/6. Help?

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- Feb 2nd 2011, 09:48 AMquantoembryoIntegration by Parts

In the answer, there is no -1/6. Help? - Feb 2nd 2011, 09:52 AMTheEmptySet
- Feb 2nd 2011, 09:54 AMquantoembryo
So would you always get rid of terms without a variable?

- Feb 2nd 2011, 10:00 AMTheEmptySet
Remember that anti derivatives are only unique up to an arbitrary constant.

You can check that you have a correct answer by taking the derivative.

Notice that if you take the derivative of or both derivatives are zero. Also notice that if you were given limits of integration you would end up with

In my opinion I always combine constants in my - Feb 2nd 2011, 10:02 AMTheEmptySet
Also I just noticed I don't see where you got you . I don't think it should be there. Double check you integration done after integrating by parts

- Feb 2nd 2011, 11:38 AMtom@ballooncalculus
Possibly the OP simplified

to

which should have been

[Edit: no, that doesn't explain it.]

Anyway, just in case a picture helps...

http://www.ballooncalculus.org/draw/parts/ten.png

... where (key in spoiler) ...

__Spoiler__:

Further edit: (See below.) Yes, false alarm. Substituting where they did, the OP integrated kind of like this:

http://www.ballooncalculus.org/draw/parts/tena.png

... so the sixth was just an extra constant as The Empty Set at first thought. Pardon the fuss. (Crying)

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - Feb 2nd 2011, 11:58 AMArchie Meade