Integrals Confused Me Until I Tried THIS 🧠

Integrals confused me until I tried an awesome polynomial integration trick! My hope is that on your calc bc exam, you'll be able to crush polynomial integrals like a ninja! Ap calc can be tough, especially when learning new concepts like antiderivatives. You'll want to stick around because I'll not only show you how to quickly integrate x^n and how to better understand it, but I'll even give you a bonus tip!
0:00 - Introduction
0:20 - Assigning A Function
1:11 - Approaching Via Derivatives
2:11 - Solving For The Answer
3:20 - A Caveat: Restricting n
3:30 - Bonus Tip
5:27 - Sample HW Problem

[@NumberNinjaDave]

ANNOUNCEMENT: I'll be videos on Saturdays each week, instead of Wednesdays! Be sure to not miss a fun limit problem that I'll be publishing on Saturday, 4/20

[@lyonkang7402]

It’s n=-1! That evokes the natural log function

[@NumberNinjaDave]

Very nice 👍

[@King-sd5vg]

This video made it a little more confusing, but I'm sure once I get more context in the field of higher mathematics this will make more sense. I'm sure this will help someone else out tho!

[@NumberNinjaDave]

Thanks for the feedback! What part was confusing so I can better understand

[@King-sd5vg]

@@NumberNinjaDave Well I'm still pretty new to this whole calculus thing, for me it was easier to just take the rules of integration such as it's shown here that x^n integrated is just x^n+1/n+1, as they are, I feel like this video would definitely help someone wanting to understand the how and why, but I just saw it kind of as a formula and that's kind of it

[@NumberNinjaDave]

That makes sense! My goal was to hopefully deliver understanding and not about just showing the quick formula because then if someone forgets a formula on an exam, they know how to derive it

[@King-sd5vg]

@@NumberNinjaDave yep, that’s a very solid approach! Definitely remember that one time I derived a formula for the length of a wave once in physics class, felt sensational! But yeah I think this will definitely work for someone, but most of the time I’ve felt that to understand stuff like this I need good knowledge of the subject before hand

[@NumberNinjaDave]

@@King-sd5vg I've been out of undergrad since 2005 and am a software engineer now. I STILL get that feeling when finally solving some coding issue. It's honestly the best

[@NumberNinjaDave]

QUIZ: Does This Work For All Values Of n? Why or Why Not