Great problem! If the constant of integration is taken as C=0, this is precisely the incomplete beta function, B(x;3/2,3/2). Taking x=1, we get B(3/2,3/2)=pi/8, which matches the antiderivative found here. Bravo!
Hi Professor V, thank you for your new video. I used the same method as yours and got the same result. I am looking forward to watching your 2nd method. Cheers.
I first simplified by multiplying the radicands, then completed the square. From there, I used trigonometric substitution and ultimately arrived at (1/8)(arcsin(2x-1)) + (1/8)(2x-1)*sqrt(1-(2x-1)^2) + C I may have made an error, though :)
Hey, I have a quick question. Do you cover everything in the playlists that are in the textbooks written? For example precalculus playlist, calc I and II stuff?
Pretty much, yes! Every topic that is required to be covered in the course outline of record. Some “optional” sections are skipped but I cover the entire curriculum.
@@mathwithprofessorv thank you very much! I asked this because I want to strenghten my basics, since I have my math classes incoming ( calc I and II), but the profs make it quite hard.So the videos should be enough right? Thank you so much for these helpful videos, we really appreciate it!
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Great problem!
If the constant of integration is taken as C=0, this is precisely the incomplete beta function, B(x;3/2,3/2). Taking x=1, we get B(3/2,3/2)=pi/8, which matches the antiderivative found here.
Bravo!
Thank you, Dr. V!
You're most welcome!
thank you professor
Hi Professor V, thank you for your new video. I used the same method as yours and got the same result. I am looking forward to watching your 2nd method. Cheers.
Great! I’m curious to see which method you prefer!
I first simplified by multiplying the radicands, then completed the square. From there, I used trigonometric substitution and ultimately arrived at (1/8)(arcsin(2x-1)) + (1/8)(2x-1)*sqrt(1-(2x-1)^2) + C
I may have made an error, though :)
Ah I’m doing that method next! The two results are similar but not identical so don’t worry. 😉 Stay tuned for the upload!
Hey, I have a quick question. Do you cover everything in the playlists that are in the textbooks written? For example precalculus playlist, calc I and II stuff?
Pretty much, yes! Every topic that is required to be covered in the course outline of record. Some “optional” sections are skipped but I cover the entire curriculum.
@@mathwithprofessorv thank you very much! I asked this because I want to strenghten my basics, since I have my math classes incoming ( calc I and II), but the profs make it quite hard.So the videos should be enough right? Thank you so much for these helpful videos, we really appreciate it!
Pretty sure I died at about 6 mins