![]() Zero because P is a polynomial, it has, ah, highest power. Then I'm going to have another derivative, another derivative, and sooner or later I'm eventually going to get down to wear it. So what happens is I'm going to start with my P. So if I differentiate a constant, I get zero. Eventually I'll get all the way down toe where I have, like a whole bunch of stuff like end times n minus one times bah, blah, blah, blah, blah all the way down to x zero. If I differentiate that again, I have n times and minus one x to the n minus to now. So I differentiate x the end that comes X to the n minus one. P of X is a polynomial, so it has some power. On the reason why is if I draw my table and I have p of X here and cute of X here. Can we use tabular integration to solve this problem? And I'm gonna claim the answer is yes. So using this information here when P of X is a polynomial and Q of exit is a function that could be repeatedly integrated. Because then we'd have zero times our final thing. Plus, we have kind of like an alternating sign going on with these and our final integral would be something like F times like this, integral of G minus, whatever f prime times, the double integral of G all the way down to when we reach zero. So we have, like something f g and then we integrate its like integral of G that we have, like another integral of G all the way down However many times. Our function that we're differentiating eventually get to zero down here, and then when we get to zero, we start with our original function f we draw some lines. Then we have on this side the function we're integrating, and the way that we set this up is we want tohave. So basically, we draw a table and we have one function here. ![]() So for the those of you who don't know, tabular integration is a way of doing integration by parts over and over and over again. And so the question that I have, um, is can I use tabular integration to solve an integral of this form where P of X is a polynomial and Q Vex could be repeatedly integrated. ![]() If X is a polynomial and cuba vax eyes some function, uh, that could be repeatedly, uh, integrated. Two functions p of x times Q of x DX where p of X is a polynomial. Today we're going to be looking at an integration by parts proof Our problem onda problem we're gonna look at It's a really general one. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |