Trigonometric integrals - sin^mcos^n, odd n (KristaKingMath)
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- เผยแพร่เมื่อ 19 พ.ย. 2024
- ► My Integrals course: www.kristaking...
Learn how to find the integral of the product of a higher order sine function and higher order cosine function. In this particular example, we'll talk about the method for finding the integral when sine is even and cosine is odd.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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This channel is making calculus more straightforward. Good explanations at each step
I would say it depends on what your professor wants. If your professor requires you to show your work, then you may not be allowed to use the reduction formula, and instead be forced to work it out normally. The other thing is that it's really difficult to memorize lots of reduction formulas. You can try to memorize as many as possible, but if you run into an integral you haven't memorized a formula for, you'll need to do how to do it normally.
Thank you. I'm so glad you like my style, and I really appreciate the positive feedback. :)
The only pi you could have factored out was the 1/pi that we factored out after the "k-substitution" in this problem. The pi inside the sin and cos functions, ie sin(pi(x)), can't be factored out. You can never factor out something that's inside a trig function like that. Hope that helps! :)
This might be irrelevant but your u in "u=sink" is perfect! Great video very thorough explanation
Thank you so much! I'm actually in class right now learning through your videos because unfortunately I cannot understand my professor. His work is very sporadic and hard to follow.
You are very much appreciated!
Sorry to hear about your professor, but I'm glad I can help along the way!
Awesome detailed explanation!
It is great that you solve problems step by step, so students don't get confused. and btw, you have a beautiful smile :)
I always hated when steps were skipped, so I do my best not to do the same. I'm glad the videos help!
thank you very much; that's a huge compliment because those guys are great!! :D
I'll be looking forward to it! Calc 2 will be my main focus next semester. :)
I'm gonna use this to build a time machine, then go back in time, slap my Maths lecturer in the face saying, "See!!! You don't have to make it look too complicated just to look smart in front of the kids you don't even know!!"
That said, thank you.
Thanks for another great video! I hope you have a wonderful holiday and get everything you want for Christmas!
you delivered awesome lecture....thank you
Happy holidays to you! :D
Why did I just find these videos the day of the calc 2 final haha... good stuff!
Good luck on the final! :D
Perfect I understood it very well!! Thank you once again! Oh, Merry Christmas and happy new years to you! Hope to learn a lot more from you next year!
you are one smart girl! your methods are excellent keep going you will be the next patrickjmt and khan.
That sure helped me. Thank you for your time.
Oh good! I'm so glad it helped! :)
Better than the Khan Academy! Love it. :)
I'm honored, thank you!
You are going to be of so much help , thanks a lot for taking the effort to mske these videos , 😊
My pleasure, Surkew, I'm happy to help! 😊
Wow thats great! Odd enough I will be taking Calc 2 next semester!
Your better than PatrickJMT and Sal Khan. Khan is a genius but he beats around the bush alot which causes him to take a long time to teach you something, although he teaches it very well. PatrickJMT teaches well and fast but sometimes he is unorganized and has holes in his explanation. You are the best of both worlds, you teach the material quickly and yet somehow you explain every every last detail as well. Very organized setup of problems too, major props
You very well may get me through Calc II... Just saying... Thank you so much!
I hope that's the case! :D
Indeed helpful. :)
Love from Philippines.
:D
Thank you for your video. Can you please inform me the program you use to make your videos.
This was really helpful. Thanks :)
Glad you liked it! :)
holy moly thank you...
very nice explanation
+Anas Kodematee Thanks!
This just might be my first youtube comment ever, but I owe you many thanks for your videos to not say something! Again thank you!
Thank you for saying something! I really appreciate it. :)
sketchbook combined with screenflow. :)
You too! :)
Perfect! :)
Thank you again :)
This is more cool and interesting then it is hard.
I have a question about the derivative of sine and cosine because I have been seeing this alot and I have to say I am a bit confused. I take online classes and for some reason I have been shown that sin= -cos and sin=cos so which one is it or is it interchangeable for whatever fits the equation? Because I thought cos= -sin and sin=cos! It's throwing me off a bit. Oh btw the way you explain things is amazing keep doing what you are doing you are a big help to many people out in the math world.
What about when they are both odd? I'm finding alot about 1 even and the other odd or both even and not finding both odd
What pen/tablet set up do you use? Also, thanks for the vids. You've been my math professor since College Algebra.
I use Bamboo, by Wacom. This page explains exactly how I make my videos, in case it helps! www.kristakingmath.com/my-videos I'm so glad the videos have been helpful! :D
I like it
:) Thanks !
subscribed
could I have factored out the pi?
Why is there do much step and identies teach in precalculus used for integration how can identies be memmorized
Do you have page on Facebook
does it matter if sin is even or odd and cos is even or odd? i'm confused
is cosine is odd, then sin can be even or odd and you can still use the method in this video.
What if you have m & n being higher number such as 7 and 8 do you still follow the same principle? or is their another way of doing it?
+xarlos789 You can still follow the same principle!
+Krista King | CalculusExpert.com can you still do it with m and n being odd ? and high numbers like 7 and 5.
+mark rainey Yes you can. As long as n is odd, m can be either even or odd, and this will still work. And you can do it with any exponents, whether large or small.
+Krista King | CalculusExpert.com thank you
I'm confused. I thought the identity for cos^2(x) was 1/2(1+cos(2x))? Is 1-sin^2(x) just another identity for it?
Jwwooten95 Yep!
integralCALC Oh ok, thank you!
happy new year -- please pray to God to solve my problems in 2015