yes, I got this one right. I just forgot the fact that ln(2) + ln(3) = ln(6), thank you so much Prof.V for taking the time to make us a video really enjoyed it so much.

Dear Prof.V I hope you are doing well, I really enjoy doing this one I got 1/2 +2ln(2) + ln(2/3) let me double check by enjoying the video.

Suppose Z=f( x(t), y(t) ) , Then (dz/dt)=(dz/dx)(dx/dt) also (dz/dt)=(dz/dy)(dy/dt) , is it correct ?

What happened to ur trig integral vid?

I solved it alittle differently I turned 2sinxcosx to sin2x then I let u =2x so du/2=dx and then I multiplied the numerator and denominator by (1- sinu) and got 0.5 integral of ( sec^2(u) -sec(u)tan(u) ) so my final answer was 0.5( tan(2x) - sec(2x)) +c did I do something wrong ? 😭😭😭

❤

PROF UR LESSONS are stunning but 3 months i will be very busy KEEP UP MAKING new VIDEOS am gonna watch old and new LESSONS after 3 months)

You’re amazing pls never stop doing videos😭

Uhh I converted the 2sinxcosx to sin(2x) and got a different answer… Is there something I’m missing? Am I not allowed to do that? 😭

Awesome!

I'm marathoning all these "integral of the day" videos years later and they're great. I always try to attempt them first before watching. For this one, I went a totally different route. I rewrote the numerator of the fraction as (1 +e^x - e^x), and from there converted the fraction into 1 - e^x/(1 + e^x). Then I let u = 1 + e^x, du = e^xdx, giving me 1 - du/u. Ended up with the same answer!

in general if u have anything like integral of 1/(linear function in terms of cosX and sinX) you can just write sinX and cosX in terms of tan(X/2) and proceed (basically weierstrass sub) sinX = 2tan(x/2)/(1+tan^2(x/2)) cosX = (1-tan^2(x/2))/(1+tan^2(x/2))

yes, option 2 is awesome I have never seen it before once had that there is something like but to see it in action just saw it now thank you so much.

wow option one is very creative!

Dear Prof.V, I hope you are doing well. For this one, I expended (sinx+cosx)^2 to (sin^2(x) + 2sin(x)cos(x) + cos^2(x)) then to sin(2x) + 1 after that I times by 1 = (sin(2x) - 1)/(sin(2x) - 1) then I got two integrals. 1 was the integral of sin(2x)/(sin^2(2x) - 1) which gives - 1/2 * 1/cos(2x) + C1 . 2 was integral of -1/(sin^2(2x) - 1) which gives tan(2x)/2 + C2 therefore, my final was = - 1/2 * 1/cos(2x) + tan(2x)/2 + C thank you so much for the integral of the day, let me enjoy the video.

I didn't know the Weierstrass substitution and I was a little bit lost with this integral, looking for some trig identities😓

Amazing idea I'll enjoy it)

Which method do you prefer? Have you seen the lovely Weierstrass substitution before? Let me know in the comments!

Oh hi my LOVELY PROF V☺

watched all of chap 16 help me get through the final 😁😁

Hi, ive never seen differentiate both sides when on "u^2 = x + 3" why do you do that?

my final is in 2 hours 🙁🙁 i’m so scared i failed my precalc final

I was putting off learning this for so long...thank the lord for Professor V!!

I know the answer is 'no' but... I was wondering what would happen if you let y = 4cos instead of 4 sin. Would it still work? And if not, why not? I'm sure you're busy and I'm not actually expecting an answer but my mind just dwells on stuff like this sometimes.

13

35:21 “do you remember??” Nope, skips 😂😂

final in 2 hr i’m so cooked i need 136% to pass the class (the final only goes up to 108%) COOKED!!,

❤❤❤❤

bravo 🙌

Hi Professor V, thank you for your new video. I did the same and got the same result as yours. Cheers.

Just wanted to come back and say that I aced my final! Your lecture series definitely made my Calculus journey a lot easier and much more enjoyable! Thank you Professor V!

Problem ending at 15:08 👌

Man this question looks so much easier than the ones I got on my final 😢

Hi Professor V, I just took my Calc 2 final last week, and I wanted to say thank you for all the help your videos gave to me this past semester! I was having a hard time understanding a lot of the sections until I started watching your videos. I’m happy to say that, with the help of your videos, I was able to get over a 90% on the final and in the course 😊 Next semester I’ll be taking Calc 3, and I’m already prepping for it with the help of your videos :)

Watching these during winter break in preparation for dif eq in the spring. I haven’t had to do an integral in 2 years😭

Thank you.

Hiya! For the second integral we could just take u = e^2t and solve. Using that we wont have to use partial fractions and it is much more convenient .

watching this day of my final, thanks for being the most comprehensive math professor I’ve encountered in my lifetime

I first solved it with pfd and got what you got but then I thought maybe I can add and subtract 2 in the numerator ... could this way also work ?

ARMENIA 🇦🇲 IS PROUD of HAVING U❤

Are you done with finals??? Or still reviewing? Let me know in the comments below! 😃

Great❤

🙌🤝

You are the best!❤

Plz. Part2

I love how U put eyes on important complicated parts☺

Great video thanks!

MANY THANKS 👏🏻