Evaluating Integrals With Trigonometric Functions

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]

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[@ProfessorDaveExplains]

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

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[@UglyStru]

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

[@ivoryas1696]

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

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

[@DBear8008]

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

[@priyamuskan5468]

Thank you so much sir.

[@lalahappy6779]

Thanks for the explanation 🌹

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

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Chemistry physics and now calculus??? Mah mannn!

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[@PreciousEkpenyong-wq2zw]

Thanks a lot, I really understood 🙏

[@sophieroot6657]

THANK YOU KING

[@AbdUllahKhan-kx6en]

It's easy to understand 👌

[@Salamanca-joro]

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

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I watched it twice and I took notes.

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Thank you so so much 💗💗💗

[@cassandraguzman2316]

thank you

[@zorozoro1442]

perfect!

[@littleretroship6403]

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

[@NoActuallyGo-KCUF-Yourself]

Don't worry, it gets worse.

[@littleretroship6403]

@@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]

@@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

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tysm!!!!

[@atchuk9045]

Nice

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thankyouuuu

[@obaidaljabry3899]

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

[@taliyamurad8208]

I Like it 😍

[@vashman01]

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]

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

[@NoActuallyGo-KCUF-Yourself]

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

[@An_ony_mous]

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

[@satbirsingh7269]

Hello sir! How r u???!!

[@tturkuaz]

Probably ı will pass the class with you

[@topiado2073]

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

[@ProfessorDaveExplains]

Sorry I’m not sure what you mean.

[@topiado2073]

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]

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]

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

[@BenGoroshnik]

@@topiado2073 wtf

[@rjf5790]

can we prove this using the U-substitution?

[@NoActuallyGo-KCUF-Yourself]

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

[@furejul7619]

you teach great and i understand.but you dont teach all the trigonometry identities making me hard to relate in in your question

[@mscience8806]

Math is CRACK to me !,, thank you!,,,!,

[@tGoldenPhoenix]

Done.

[@tGoldenPhoenix]

Done comprehension.

[@smookytubes]

Can you do some problems using u substitution with trig integrals?

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[@TheFirstNamelessOne]

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

[@kbailkeri]

He already explained them in this video, kzbin.info/www/bejne/lYvUlKuYn9-srsk

[@NoActuallyGo-KCUF-Yourself]

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

[@kzkaa.]

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]

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

[@Baburun-Sama]

"Sine! Cosine! Tangent! Integral! Permutation!" - Ringo Ando

[@aradan4955]

You didn’t do tan

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thank you jesus!

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You shed what you write we can't see

[@ambervancott3486]

;)wink wink