please let your students use the DI method for integration by parts

0:00 please let your students use the DI method
0:17 integral of x^2*sin(x) with the DI method
1:20 integral of x^2*sin(x) with the u-dv format
7:11 integral of tan^-1(x)
12:18 integral of e^(-x)*cos(x)

#calculus2 #calculusteacher

[lordstevenson]

You couldn’t resist the +c. Was getting worried for a sec.

[blackpenredpen]

Imagine if a student makes a video saying "please let us use the DI method" for 3 hours...

[yungy]

I learned the DI method from your channel, and my teacher would always get so angry at me and automatically deduct marks if he ever saw me use it. He used to solve integrals on the board in class and one integral had the entire class stuck. Me and my friend (who watch your videos) solved it using the DI method and we showed him and he just disregarded it because it wasn't the method on the syllabus. Maths is maths, if you get the right answer then why does it matter what method you use (as long as it isn't just a fluke of course). Love your videos, keep up the good work!

[dutchjack]

Wow, one of my students did this last year and I was astonished by it - I gave them full credit without fully understanding why they did it. Glad I came across this video!

[amitavadass]

We miss you and you mathematics for a long time!
Love from INDIA!

[noahtaul]

As a lecturer, let me explain my beliefs. I would have no problem with my students using this DI method on the test or on homework (although I have a grader, so I'd have to explain to the grader what the DI method was). But in the textbook we use, integration by parts is only a single section among 25 that we have to get through, so it takes up a single day, maybe 2 problems on the homework, and maybe 1 problem on the test. So it's not strictly necessary for students to spend multiple hours trying to improve their speed at integration by parts, because we just don't do it enough. Of course, BPRP has done millions of videos on integration by parts, with varying levels of intricacy, but in comparison to u-sub, IBP doesn't come up nearly enough for an "increasing speed" argument to justify me spending class time to teach the DI method.

I also believe that the students that I teach prefer structure over speed, because math is confusing, and once you have rules you know can work, I imagine that you'd be happy to stick with them. The DI method looks like magic at first; you write down a bunch of functions, take their derivatives/integrals, and calculate a final integral at the end, and you're done? Why are these pluses and minuses there? Why do we multiply the diagonals, but then we have to integrate along the bottom row? Each of these questions makes it more likely that they'll forget how exactly it works during the test, whereas the structure of int udv=uv-int vdu is simple enough that students will remember it. And the usual u-v method arises directly from the product rule, so to make things rigorous in class we have to teach it this way first, and then do examples to show how IBP works at all, and then there's not nearly enough time left in class to explain the DI method.

I will say, though, in my class last year, I sent out a link to your earlier video explanation of the DI method, so students could watch and learn it themselves, if they were really motivated. I didn't mention it again, so I guess I didn't really legitimize it. Next time I teach integral calculus I'll write a homework problem that involves multiple integrations, and in the instructions write "You can either use the DI method from the video or repeated integration by parts." This will prompt them to actually watch the video.

[michaelchung]

This is one of the best explanations of the DI method that I have seen on YouTube. In other YouTube videos, they will just teach you the DI method without explaining why all the diagonal lines and the "tie-off method" and the plus/minuses work. And you are pretty much the only one out there that actually explains in a really concise way where the DI method actually came from by comparing it to the traditional u-dv method, and now it just all makes sense to me now, so thank you. Keep up the good work!

[jagatiello]

That final +C addendum just make my day...

[gravity_well]

Every dislike is a teacher who doesn’t want to change their answer key.

[shashankdesai]

yesterday i surprised my teacher by doing a 7 mark integral in 1 minute using DI method
his reaction was epic XD

[blackpenredpen]

“Knowing the DI method doesn’t guarantee that you can pass calc 2, just like knowing the power rule doesn’t mean that you can pass calc 1”

...bprp

[adamkadaban]

lol I'm gonna send this to my teacher

[rohitchaoji]

DI looks like a compact way of doing exactly the same things as in integration by parts. It reminds me of an equivalent to how matrix operations are just another way represent linear equations or how different formulations of quantum mechanics all represent the same things but differ in complexity of representation.

[pacolibre]

Just call it “Tabular integration” and they’ll catch on. Thats how we learned it

[jordimayorgisbert]

I'm using it since 2018, when I saw your awesome video. Many teachers think about any kind of magic on invented maths. Very unhappy with these teachers. I'm trying to make my colleagues understand this awesome procedure. I'll help you with this task, sharing it. Thank you for your big work !!!

[HeyKevinYT]

I wasn’t prepared for the “d equal sign” 😂

[noahali-origamiandmore]

I nearly got a heart attack when he didn't put +C after the last integral. I was relieved in the end.

[kingarthr]

I think this method is good to learn after you learn the original technique because it might feel random if you just started with this although most calculus classes already do that with the u dv formulas. But it isn't obvious on why this works if you're just given the technique. I do think that this method will become commonplace in just a few years with everyone spreading awareness.

[AlexWa]

I literally just had this question as a homework problem. Thank you for explaining this!

[japotillor]

In my classes I teach both, I prefer DI method when there are multiple steps involved...I use the the traditional method for one step problems...As long as students show their work, I don't make a big deal of how they get the answer.