Trigonometric Integrals
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- This calculus video tutorial provides a basic introduction into trigonometric integrals. It explains what to do in order to integrate trig functions with even powers and how to employ u-substitution integration techniques and power reducing formulas in order to find the indefinite integral of trig functions with sin and cos. This video contains plenty of examples and practice problems.
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• Trigonometric Integral...
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Professor Organic Chemistry Tutor, thank you for another fantastic video/lecture on Trigonometric Integrals in Calculus Two. These integrals are built off of Trig Identities and pattern recognition. All students in Science and Engineering should memorize all the Trigonometric Identities from Trigonometry. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
Georgesadler7830, thank you for yet another amazing comment/remark on this video/lecture on Trigonometric Integrals in Calculus Two. Your statements are well thought out and accurately composed. Anyone who watches Calculus Two videos by Professor Organic Chemistry Tutor should like your comment. This is an error-free comment on TH-cam TV on the video/lecture on Trigonometric Integrals in Calculus Two by Professor Organic Chemistry Tutor.
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List of 0:36 trig identities, 1:12 double angle identity, & 1:47 power reducing formulas to memorize
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@17:00 you say negative cos(2x)'s derivative is negative sin(2x) when it should be positive sin(2x)
Okay I'm glad someone else saw that
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no its not positive sin, its negative because the derivative of -sin is -cos
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Like the way you explain this Mathematical concepts. I like you and be blessed. You always my teacher in this area of calculus.
I would recommend going the extra step in some of your less popular videos and include more difficult problems towards the end. I would have been very happy to see a sec^2 x integration in this video. Keep it up though, overall you do a fantastic job with your videos.
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Memorize your chebyshev polynomials, folks. In matlab, I have functions that generate chebyshev matrices and the inverses to convert between cos nx and cos^n x. I've found that asking it to integrate cos^n(x) takes way more processing power than just converting it to the equivalent chebyshev form and then integrating.
Also useful for definite integrals of the form sin^a(x)*cos^b(x) or sin^a(x)*cos(bx) (or similar) is the beta function
en.wikipedia.org/wiki/Beta_function#Reciprocal_beta_function
Both are closely related and you can modify one to get the other.
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9:00 what a coincidence I am having the exact same issue with this problem and I’m working on it rn! Thank you!!
In 25:00 you can just easly add 4 and divide by 4, so you have inside integral:
4sin^2cos^2
And that is
(2sin cos)^2
Which is
(sin2x)^2
Thank you so much! I managed to answer my assignment well.
Again, thank you! I just answered my quiz well. This video really helped.
how do you know when to use power reducing, half angle, double angle, formulas and pythagorean identities?
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at 30:25 he uses the rule that (1/x)=lnx, but isnt this rule only meant for linear equations? cosx is not a ljnear equation so we shoulnt be able to use it at all, or is there an exception when we use the u-substitution method?
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Thank you professor.
Integrate (sin^5 X cos^3 X dx) at 15:00 what about if you split sin^5 X to give you ( sinX sin^4 X ) instead of cos^3 X and make ( u= cos X).
Here what I figured out is that whichever you make (u to b equal to) is the one to be on the final answer after integrating. I got (-1/4 cos^4 X + 1/3 cos^6 X - 1/8 cos^8 X + c) as my answer.
Can you explain me why the two methods show different answer please
Please Sir those it mean that in this question the final answer can be in (sin X or cos X ) depending on which one you split
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why does 1 turn into U when integrating?
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Trigonometric integrals make me wish I was a humble berry picker living 2 million years ago
my answer to the last question was ln|secx| + cos(2x) / 4 +C
good delivery of concepts....thank you so much
Are there two different answers depending if we choose the variable u to be sinx or cosx? And are they both correct either way?
It depends on the function in your integral. Some can only be done one way, but there are some that can be done two ways depending on what you choose to be your u. In the second case, yes, there could be two different answers, but they would ultimately be equal. They would be different forms of the same answer. Hope this helps!
@Nuzaer Bari Glad to help!
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26:19 how (1-cos^2(2x)) becomes sin^2(2x)
This is the only part of calculus that I am not good at. Maybe I should have learnt trigonometry at school.
For the question integral of sin^2 x dx why do you divide sin(2x) by the derivative of 2x? (ie 2) instead of multiplying by two?
This has really helped me, thanks to you sir👌
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What technique do you use to determine which one will be U??????
At 16:22 how do you know when to make sin^2(x) equal 1/2(1-cos^(2x)) or when to leave at as (1-cos^2(x))? I'm really curious to know. Thank you in advance for your help.
Because we do not know the integral of sin²x, we only know the integral of the following trigonometric functions:
∫ sinx dx = -cosx + c
∫ cosx dx = sin + c
∫ secx dx = ln|secx + tanx|
∫ cscx dx = -ln|cscx + cotx|
∫ tanx dx = -ln|cosx| + c
∫ cotx dx = ln|sinx| + c
In addition to 4 other integrations ,Therefore, any conjunction other than them, we need to convert to one of them. How? Through the Trig Identities you have to save them
18:07 cos^(2)3x
13:06 sin and cos exponents odds
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The best playlist on trigonometric integrals th-cam.com/video/HHuiSetD-6w/w-d-xo.html&ab_channel=BiPhysiMath-Special
You helped me once again, thanks!! Cheers!
nice, stay curious
This video was definitely helpful, but knowing which identity to choose is still sooo confusing. I'm definitely not gonna do too hot on this exam lmao
Yes, that is arguably the most difficult part, but generally I have found that when you split odd powers of sin and cos, you always want to use pythagorean identities, and if you just have even powers in your original integral, then you will want to use the half angle identities he shows at 1:20. I have my own video on this topic where I explain this in detail and make it clear when to use each identity, I will link here for you. I know you commented this a few days ago now, but hopefully this helps you in time for your exam! Link: th-cam.com/video/diRi35CUebg/w-d-xo.html
@@JKMath hey thanks for the tips! I'll check out the video because I know these integrals will be coming back to haunt me 😥
How do you know when to use integration by parts or u substitution?
at 30:37 why you used lnu ?
at 17:05 why did you divide by 2? I've watched this part 6 times and cant figure it out
it is just like integrating cos(2x).
the integration of cos is sin
however, we need to derive the inside cos
let u = 2x
du = 2dx
du/2 = dx
sin 2x = cos 2x du/2
= cos2x/2 (du will cancel because you integrate the cos already)
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8:24 why is that cos^5 you held it was u^5 instead of dividing them into cos^2[x] cos^2[x] cos[x] sin[x]
Wonderful explain sir
How come the answers are different when u let u =cos x??? I mean how should we know ,this one is the one to use in the exam???
thank you
Could you properly foil instead of saying we did this last time
Find \int tanx^(5) \theta sec7^(2) sec \theta d \theta
Thanks a lot.. Really helpful..
Should you really use Power reducing formula at all times?
Why do you put cos in absolute value at the last question can someone explain me
2024 still using this
question in 29:28, couldn't we have used the double angle formula of sin^2(x) to cancel the cosine in the denominator???
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11:05 canceling out sin you forgot the negative
ok just continued watching, he remembered
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better method to integrate 3 4 n root of a number is to use eleur theorem
Can someone work this question out and break it down for me I’m new to these stuff and I’m still learning integral of (sinx+sinxtan^2x)/sec^2x thanks in advance
Thank you.🌷
@theorganicchemistrytutor on the problem at the 15 min mark i solved it by splitting up the sin^5 and setting u equal to cos but we got totally different answers. how is that so?
at 11:00 i said cosx^2 = 1 - sinx^2, result was different but i think this must be true too ._.
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I can pretty much do Integrals and derivatives very well. But I become stupid when the problems are trigonometry, exponential function, or logarithms.
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