#Integration

13 messages · Page 1 of 1 (latest)

cursive pine
#

Could someone explain me why the following is? For integration of rational functions, we have like 3 cases, but why is that if you have repeated factors you multiply by the first power,... and why do you have Bx+C when the denominator is irreducible. They have always taught me that trick but I never understood why that is.

Thanks for helping!

velvet marlinBOT
#
  1. Do not ping the Moderators, unless someone is breaking the rules.
  2. Do not ping the Helper Moderators, unless there is a conflict between helpers.
  3. Do not ping other members randomly for help.
  4. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
  5. Wait patiently for a helper to come along.
  6. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

tranquil dune
#

@cursive pine be more specific, provide examples this is too vague

cursive pine
#

how do I understand the fact that (x-1)^2 should be done twice

#

when its a repeating factor

tranquil dune
#

and let me know if any confusion still persists

fickle knoll
# cursive pine how do I understand the fact that (x-1)^2 should be done twice

It might be instructive to try and do the top example without the first A term. Just to see how things work out if you dont have it there. Also try to think about the reverse process, to go from a decomposition back to the original fraction you multiply the top and bottom by the polynomials in the other parts. But of course for the A term you only have to multiply by (x-1)(x+1) and you only have to multiply the B term by (x+1). What does this mean for the maximimum degree of the top of the B term after you multiply?

#

I think you could actually write the first example like the second, with a degree one polynomial in the numerator. Though you want to avoid this when possible to make the integration easier

rugged ventureBOT
#

@cursive pine

<:HelpIcon:1304095958283321385>| Help Reminder

Hello reyess77, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.