Evaluating Integrals With Trigonometric Functions

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6 жыл бұрын

Now that we have the basics down regarding integration, it's time to start looking at trickier functions, and eventually more complex integrands. First, we will see trig functions inside integrands all the time. How do we integrate these? Well if we remember the derivatives of the trig functions, it won't be too hard!
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@vex3315 6 жыл бұрын

This is a lifesaver for me. This is actually one of the topics that I couldn't grasp a few weeks ago and this week is already our finals. I am a SHS student in the Philippines and I am frequently using your content to learn in advance or study the topics for our quizzes so I am grateful to you Sir! I hope I can help directly by giving donations but I make sure I share your videos to my classmates. Thank you!

@ProfessorDaveExplains 6 жыл бұрын

Awesome! Any donations to my Patreon page are most appreciated! But failing that just tell your friends to subscribe :)

@shrimpjar3612 Жыл бұрын

I'm in Southern New Hampshire university and I cannot believe how much this video helped me! I couldn't understand my professor at all without this.

@kiransingh2225 Ай бұрын

what are u doing now?

@adhel-estebanriverarodrigu2234 Жыл бұрын

DUDE! You seriously have a gift of teaching! I was thinking of dropping out of Calculus because I didn't understand anything, and with this video, and reviewing the video you recommended, you got me up to speed in less than a day!!! YOU ARE A LIFE SAVER!!!! Thank you so much for what you do!!! Keep up the great work!!!

@UglyStru 2 жыл бұрын

This video should be shown to every trig/calc student ever. Thank you for this, Dave. You're helping me tremendously

@ivoryas1696 2 жыл бұрын

UglyStru Not too sure about every _trig_ student, lmao, but that is true.

@Bankosek 6 ай бұрын

I love your modern content, but those tutorials will stay relevant and great for ages.

@Salamanca-joro 5 ай бұрын

Absolute legend man i watched multiple videos and you were one of the few who could explain it cause i was lost

@priyamuskan5468 6 жыл бұрын

Thank you so much sir.

@lalahappy6779 3 жыл бұрын

Thanks for the explanation 🌹

@DBear8008 2 жыл бұрын

I missed the class where we talked about this stuff, and I have been singing the intro song all day in anticipation for doing my homework on this

@PreciousEkpenyong-wq2zw Жыл бұрын

Thanks a lot, I really understood 🙏

@anthonyvicker8033 3 жыл бұрын

Wow! This is really good sir. From Kenya( Africa)

@sewwandiishara9828 3 жыл бұрын

Thank you very much sir...(from sri lanka..) 3month lecture in 10min.. 🙏👍👍

@dinidunisal4648 2 жыл бұрын

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@user-gt2us8qc9n Ай бұрын

Thank you so so much 💗💗💗

@francisgregoryku1689 5 жыл бұрын

Chemistry physics and now calculus??? Mah mannn!

@elimarburger1659 4 жыл бұрын

he knows about a lot of stuff

@sophieroot6657 3 жыл бұрын

THANK YOU KING

@kaihsu_angels 4 жыл бұрын

Just subscribed 😊

@Salamanca-joro 4 ай бұрын

5:44 or we can also say sin^2x/cos2^x which will be[ tanx] and cos^2x/cos^2x will be 1 and we will get : The integer tan^2x+1 which will be the integer of sec^2x which is tanx+c

@nayanpatel312 3 жыл бұрын

Simply, Awsm

@zorozoro1442 2 жыл бұрын

perfect!

@AbdUllahKhan-kx6en 5 жыл бұрын

It's easy to understand 👌

@cassandraguzman2316 3 жыл бұрын

thank you

@alyrainnee4939 6 ай бұрын

tysm!!!!

@mc2092 4 жыл бұрын

Need more videos 😭🥺🙏

@aselim20. 6 ай бұрын

I watched it twice and I took notes.

@lazyonigiri5665 2 жыл бұрын

thankyouuuu

@littleretroship6403 2 жыл бұрын

Holy cow this is hard. I can’t imagine how integration is gonna be later on

@NoActuallyGo-KCUF-Yourself Жыл бұрын

Don't worry, it gets worse.

@littleretroship6403 Жыл бұрын

@@NoActuallyGo-KCUF-Yourself my then 13 year old brain was too stupid to handle that but now I’m a cool 14 year old so I think I should be able to handle it. (Plus I don’t have much time left on this earth since im an old man)

@ultimatedoug2227 Жыл бұрын

@@littleretroship6403 damn bro you learning integration at 14? bruh i wish i hadnt wasted my time doing BS. ill use this as an insipiration and work more

@atchuk9045 6 жыл бұрын

Nice

@obaidaljabry3899 3 жыл бұрын

how to integrate sin2x/(1+cons^2)

@topiado2073 5 жыл бұрын

Sir would the rule of questient and multiple hold in definite integral??? Plizz...

@ProfessorDaveExplains 5 жыл бұрын

Sorry I’m not sure what you mean.

@topiado2073 5 жыл бұрын

sir will product and quotient rule be applied to definite integral..,?? Well as u mentioned that for indefinite integral there's no product and quotient rule as compare to that of derivative has... Hope u gotta point sir🙂

@ProfessorDaveExplains 5 жыл бұрын

no, integration has no such rules, which is why it's more difficult, check out my other tutorials on u substitution, integration by parts, trig substitution, these are the techniques we use when integrating.

@topiado2073 5 жыл бұрын

@@ProfessorDaveExplainssir may i hv ur contact no,...so that i could ask u problem regarding calculus sometimes🙂plizz sir

@BenGoroshnik 2 жыл бұрын

@@topiado2073 wtf

@taliyamurad8208 3 жыл бұрын

I Like it 😍

@satbirsingh7269 6 жыл бұрын

Hello sir! How r u???!!

@rjf5790 4 жыл бұрын

can we prove this using the U-substitution?

@NoActuallyGo-KCUF-Yourself Жыл бұрын

Not a proof, but you could probably use that as an alternate method to evaluate.

@vashman01 2 жыл бұрын

What to do when evaluating trig functions with respect to y? Evaluate the integral of tanxdy from 0 to 7? What about sinxdy from 0 to 7?

@multiplyx5864 2 жыл бұрын

those are definite integrals. There is a separate video on that

@NoActuallyGo-KCUF-Yourself Жыл бұрын

If the variable of integration is y, any functions of x are treated as constants.

@An_ony_mous Жыл бұрын

The answer is 7sinx and 7tanx. sinx and tanx are constants because given variable is y.

@TheFirstNamelessOne 4 жыл бұрын

Sir, could you give me the reason of this? Why do these trigonometric functions behave like this when integrated?

@kbailkeri 4 жыл бұрын

He already explained them in this video, kzfaq.info/get/bejne/lcChltuTz-DdqJs.html

@NoActuallyGo-KCUF-Yourself Жыл бұрын

What do you mean by "why"? The reason is that is what happens when you perform the operations.

@kzkaa. 3 ай бұрын

Ignore the other guy. This is actually a very good question, and it has something to do with what you're really doing when you integrate a function. As you probably already know, integration is all about finding the area of a function. One way to think of it is that whenever an antiderivative goes up, then the area underneath its corresponding derivative also goes up and vice versa. Of course, I'm no experts, so you'd have to verify it yourself.

@henrygalvan9333 Ай бұрын

You think it helps to uderstand whats happening graphically? M @kzkaa.