Integral of the Day 6.18.24 | Medium Spicy Level! What do you think? | Math with Professor V
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- Опубліковано 17 чер 2024
- Here's your latest Integral of the Day! I promised a more straightforward integral after my most recent upload, so let me know if you were able to successfully solve it on your own. It did require some attention to detail with changing the limits of integration, especially with the trig sub portion, so if you need help with that check out the video below:
Changing Limits of Integration: • Changing Limits of Int...
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doing this and then watching the video makes me so grateful for hyperbolics
Easy peasy😄
That was a good one. So satisfying when my answer matches yours. I have been doing series problems and watching your series videos but trig sub is my favorite integral technique so when that comes up I have to give it a try lol.
Yayyy so glad you liked it! I’ll do more trig sub since I love them too! ☺️
Dear Prof.V good luck with your summer school ! At least I have something to work on. you did an outstanding work with creating videos it does help a lot in university . anyways please enjoy the rest of your day
Dear Prof.V I hope you are doing well, for this one I let u = e^t and du= e^t*dt ,u(ln(4)) = 4 and u(0) = 1 and get a integral of 1/sqrt( u^2 +9) from 1 to 4. and apply u-sub by letting u = 3*tan(x) and du = 3*(sec(x))^2dx when I put everything back to the original from I got integral of sec(x) which is equal to ln|tan(x) + sec(x)| but now change from x to u which was equal to ln( (sqrt(9+u^2)/3 + u/3 ) and the deference was ln(9) - ln(sqrt(10) + 1) hopefully it is right. let me enjoy the video.
I think if you rationalize the denominator at the end, it does help simplify. Great vid like always! Enjoyed it!
Oooh now I’m mad I didn’t! I’ll have to try it to see. Thanks for the support and your comment! ☺️☺️
Hello ma'am, hope you're doing good
You too!
is ln(sqrt(10)-1) also an acceptable answer?
I was able to simplify ln(9/sqrt(10)-1) down to ln(9(sqrt(10)-1)/10-1)) which is just ln(9(sqrt(10)-1)/9) which then simplifies to ln(sqrt(10)-1)
Yes! 🙌🏻 In fact; I wish I simplified the final answer as much as you did since it’s cleaner. Well done! 👍🏻
@@mathwithprofessorv Thank you!!