Trigonometric Integrals - Part 5 of 6
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- Опубліковано 1 жов 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Trigonometric Integrals - Part 5 of 6. In this video, the 'cookie cutter' case of products of sin(mx) and
cos(nx) are shown.
For more free math videos, visit PatrickJMT.com
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11 years ago, Patrick forgot to multiply 1/2 by 1/5 ?
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Yahyah hahaha
@@ahmadzaka9885 14*
@@martinlopez4719 15
Answer key: Q1=1/2 cos(-x) - 1/10 cos(5x) + C Q2=-1/2 sin(-x) - 1/10 sin(5x) + C
ya! thanks for pointing out the mistake : ) i added annotations for it : )
congrats on the good grades!!!
you forgot to multiply the 1/5 on the 1/2
I agree with you
was about to commment that
This video's age is 11
Oh, I also saw that too, but I was like hmm.. lets go to the comment section. Oh! I was right! Yes, I'm actually learning it!
he forgot to multiply 1/2 with 1/5 to get 1/10.... it should be 1/10 not 1/5
happy to help, good luck :)
Thanks for the video, but you forgot to distribute the 1/2 to the 2nd term. So it should be 1/10th of sin(5x)
(3:20 and 5:15 )hey you forgot the multiply the 1/2 to 1/5 in both example aren't you ?
My favorite thing I've learned from Patrick aside from a ton of Calculus concepts is to use a dry erase board to do math problems.
Genius!!
great, glad to help! : )
ops! it sure is! thanks for letting me know! i will fix it
no worries! hopes it helps a bit
You are helpful sir..... THANKS
glad the videos helped!
@Digidices just wait a few seconds
yep, i have them both
Prof patrickJMT:
How about writing with your right hand?!
; )
my final answer in the 2nd problem would also be : [ 1/2sinx - 1/10sin(5x) + c ]
since : [ sin(-x) = - sinx ]
is that right ?
nope
+Aboody Yahya Yes, it is correct
u r not fully correct, cause even though its -sinx u still have to integrate it so u would get a 1/2cos(x) + 1/10sin(5x)+c
naber krdş
shouldn't it be m-n in the parenthesis
d/dx (sinx)=cosx
and d/dx (cosx)=-sinx
pls assist me in the last few steps of the first problem
and in the second problem y haven't u multiplied the last expression with a -ve sign after converting cos to -ve sin
R u not going to distribute 1/2?
@2:50 oh yeh he wrote dx instead of du he is a human.....
@2:59 oh well.... ive said nothing...he saw it....OBV
I am still in middle school! i did not start my high school yet! I plan on taking olympiads! It is All Thanks To You That I can Understand The maths behind the physics Problem! Your Calculus Class Rocks!!!
I was wondering the same thing.. and yes it should be -1/10sin(5x)
I checked it using mathematica
ugh. My teacher only spent 1 and 1/2 week on U Substitution. and went though the trigonometric integration in one day... never taught us the little side notes you had in the beginning... :(
Isn't cos(-x) = cos(x)?
Anza Khan Yes
yep
Hi Patrick, do you challenge problems involving techniques of integration(Partial Integrals, Improper Integrals, Trig Substitution etc); or just only on trigonometric integration. I find your tutorials to be very helpful :). If so, do you have a website that we could go on? Thanks :)
thanks thanks man
thanks patrick for your very very helpful solutions
I felt you rushed this a bit (something important to do perhaps?), and it showed at the end of the two problems because you didn't multiply by 1/2 for the second integrals. Besides this, you still did great. Thanks!!
The real answer for the 2nd one is: sin(x)- 1/5sin(5x)+C
oops im an idiot i assumed the negative sign was from the integral of the cos but that came from the u sub of -x my mistake, you are correct, except the whole not distributing the 1/2 all the way :P
just had a question for the second question the answer at the end. Shouldn't it be -10 sin 5x+c cause u are using the distributive property of 1/2
I HATE MATHS AND ESPECIALLY CALCULUS NOW AFTER SEEING VIDEOS ON UR WEBSITE I HAVE BECOME CONFIDENT IN MATHS THANKS ALOT!!!!!!!!!!!!!!!
i think you made a mistake in the answer.
shouldn't 1/2 multiply (1/5 cos x) to get the final answer as:
1/2 cos x - 1/10 cos x + c?
For the solution of the first problem, shouldn't the answer be: 1/2cos(x) - 1/5cos(5x) + C ?
Since cos(-x)=cos(x)
For the last one you forgot to multiply 1/2 to the second term.
for the last problem, can we just assume the cos (-x) to be cos (x) as it's an even trigo?
for the last problem, can we just assume the cos (-x) to be cos (x) as it's an even trigo?
Hey man, thanks very much for this wonderful video, I am taking calculus 2 right now for my sophmore year at the university I go to, and we only had a day and a half to learn this material before the quiz and with the help of your videos, I believe I made a 92 or higher. The Definite trig intergral got me lol, I accidentally forgot to change my limits when I performed the sub. method... well once again thanks!!
Why are you left handed :( I can't see half of the time
2024 comment :D ty for ur vids
helped me a lot hope i find someone like u in physics. Thank you.
3 years too late but check out michel van biezen, he's amazing for physics!
at 5:26, shouldn't it be -1/10sin(5x) instead of -1/5sin(5x)?
at the end for the first part where you take the integral of cos(-x) you got a -sin(-X) and pulled the negative out front to get a -1/2 sin(-x) correct? If so when you do the second part and take the integral of cos(5x) the integral should again be -sin(5x). if you pull the negative out front, shouldnt it make the second part be +1/5 sin(5x) not -1/5 sin(5x), due to the double negative?
Sweet dude, 9 years ahead of your quesion, I also thought that as well!... I probably ask my math tutor tomorrow... lol I was hmmm no... there's way lol the - times - should = a Positive +
@mrgoatsnake i noticed that too. i thought i had it wrong.
I got cos(x) in the first exercise instead cos(-x) and sin(x) in the second instead -sin(-x), but I guess it's ok since they have the same value, right?
pheew..takes a lot of work..huhuhu
Thanks Patrick..
you should replace my professor
u deserve an international distinction in maths
Same here man. I wish Patrick was my professor.
do you have vids on trig sub, or reihmann sums?
@smithsansoo - yes i noticed that too, can someone confirm bout this? thanks btw mr patrickJMT !
@shamzahm thts true...there shld be 1/10.
thanks a bunch!
@mrgoatsnake i thought i was going crazy when my answer didnt add up both times! i guess its nice to know that we all tend to make the same mistakes! also, it helps to get to your own answer, and be convinced enough to doubt the given solution. he really should update it or put a note, though!
I hope you don't mind a joke!
You could become ambidextrous!
Great videos!
In the first example in final you do not (1/2) multiplus with (1/5cos5x)
hi.. I also would like to point out that u forgot the distribution of half in the second term and also dx should be replaced by -du... you forgot minus... Mx
Thanks keep it up.
Welcome to The Future
instead of doing u-sub, you can use the fact that cosx is even and sinx is odd so that cos(-x) = cos x and sin(-x) = -sin(x)..but u-sub also works
you teach way better than my professor.... i can barely understand him.. thank you for your awesome videos! they helped me a lot
la tuya por si acaso xdd
Mine turned out to be for the second problem was -1/2sinx - 1/10sin5x +c
Dude, your videos are awesome!!! but quick question, what about when we take an integral of [cos(pix)cos(4pix) dx. pi as 3.14......etc Thanks
Not sure if this was asked before, but could all those kind of integrals be integrated by integration by parts?
great vid really helps. You should probably tell people that you forget to distribute the 1/2 though so they don't get confused.
If you get some time could you redo the video reading the comments for the correct answer is confusing. Plus I think it'll benefit everyone if you did.
I came to youtube from his channel because I had no idea why he wasn't distributing...glad i saw this comment
thanks man keep it up
did you forget to distribute the (1/2) to the (1/5) at the end of the second problem?
DUDE HOW MANY FRICKEN TRIG INTEGRAL SCENARIOS DOES THERE HAVE TO BEEEE
how many you want?
Great video, thanks! Why didn't you distribute the 1/2 through the entire answer though?
awesome thanks
Thank you alot
i thought the 1/2 was suppose to be distributed to make 1/5 to be 1/10?
Nevermind.... I just read the second top comment. I'm just going crazy
Oh the frustration of having to memorize it all; btw thanks for the help Patrick.
i love how all 6 parts of this video is only 1 chapter of my test :(
i just want to ask a question...
my prof is using this formula:
sinucosv=1/2[sin(u+v)+sin(u-v)]
so i used it.
and then I tried yours:
sinucosv=1/2[sin(u-v)+sin(u+v)]
but it had different result. how would i know which one is the right formula here?
They are the same formula
Shouldn't the (1/2) distributed to both sin in the end.
THANK YOU.. you are my virtual PROFESOR..jaja
Awesome trig integral videos, best help ive had with it are these vids
what if it's the integrall of cos^6(2x)sin(4x)
Gg calc
you are a beast
How about 1/2 ( sin A+ B ) - ( sin A+ B )?
part 4 has me completely lost
What does m and n stand for? Please reply asap. Thanks for the vids! :)
7mara kberi enty
1/10 bro 1/10
you the best
great video!
Integral of sin power 5 x+cospower 4 2x..assist me please
for that one you have to split the sinx into different powers and the same for cos2x . then use trig identities . after that solve the two products separately the same way you would shown in the sereis of videos he has. using trig powers methods
Thanks
great tut..
Thanks man..........
"Maybe I shouldn't use du again...i'm sure i'll be fine" these videos are for us, WHO DO YOU TAKE US FOR?! Just kidding, your videos are awesome, thank you very much for all the help!
Yea I noitced that too