I read multiple explanations of this that left out pieces of the explanation and only made me more confuse than when I started. This was the first source to actually make it clear what I needed to do. Thank you for the helpful, informative video!
I thought you couldn't integrate a function with its parameter as a bound? i.e. how can t be the upper bound and be part of the function at the same time?
thank it help alot i have final in 2 days time. but one quick question what if the end part of the question is change to with respect to arc length measured from (1,-1,2) in the direction of increasing t ? thank you !
Thank you very much, Your explanation was so clear and easy to follow (plus the question you solved happens to be the same i was looking at in my textbook).
Determine where on the curve given by r ⃗(t)=〈t^2,2t^3,1-t^3 〉 we are after travelling a distance of 20 units. Can someone help with the above question?
Remember that the integral (with respect to x) of 3 is 3x, the integral of -7 is -7x, and the integral of k is kx. So integrating a constant just means you need to attach the variable to that constant.
I encountered the exact problem and didn't know how to solve, came here, and found out that it is the exact problem, and even numbers match perfectly....
Some people substitute a dummy variable like "u" when they take the integral. I suspect it's less confusing to evaluate u by plugging in t than plugging in t or t. But the u really threw me the first time I saw it.
I'm confused as to why YT search for Krista's channel of "Chebyshev" gave out this video. I was hoping to get a nice example of how to use Chebyshev substitution. Not that this is not interesting, just unrelated.
Your videos are excellent. When Sal's voice puts me to sleep I can throw you in the mix and liven back up. Keep up the great work!
I've been trying to understand my textbook's version of this for an hour. This saved me! I loved how you represented t as a function of s.
sweet jesus thank you you much, multi variable calc exam in 2 hours
I read multiple explanations of this that left out pieces of the explanation and only made me more confuse than when I started. This was the first source to actually make it clear what I needed to do. Thank you for the helpful, informative video!
You're welcome, Kathryn, I'm so glad it all made sense! :)
That is so much easier that I thought. You are so good at hitting all the points, but keeping the video short. Perfect explanation, thanks.
Thank you so much, I'm so glad everything made sense! :)
Wonderfully explained!
Good example. But in order to find an integer reparametrization result , instead of Root(29), one has to find a *sum of three squares that form a perfects square*. The deravatives of 2t,3t,4t, obviously parametrize to 29, a non-perfect square. So, the whole solution for *integer* reparametrization for x,y,z < 30 are :
1 ^2 + 2 ^2 + 2 ^2 = 3 ^2
1 ^2 + 4 ^2 + 8 ^2 = 9 ^2
1 ^2 + 6 ^2 + 18 ^2 = 19 ^2
1 ^2 + 12 ^2 + 12 ^2 = 17 ^2
2 ^2 + 3 ^2 + 6 ^2 = 7 ^2
2 ^2 + 4 ^2 + 4 ^2 = 6 ^2
2 ^2 + 5 ^2 + 14 ^2 = 15 ^2
2 ^2 + 6 ^2 + 9 ^2 = 11 ^2
2 ^2 + 7 ^2 + 26 ^2 = 27 ^2
2 ^2 + 8 ^2 + 16 ^2 = 18 ^2
2 ^2 + 10 ^2 + 11 ^2 = 15 ^2
2 ^2 + 10 ^2 + 25 ^2 = 27 ^2
2 ^2 + 14 ^2 + 23 ^2 = 27 ^2
2 ^2 + 24 ^2 + 24 ^2 = 34 ^2
2 ^2 + 26 ^2 + 29 ^2 = 39 ^2
3 ^2 + 4 ^2 + 12 ^2 = 13 ^2
3 ^2 + 6 ^2 + 6 ^2 = 9 ^2
3 ^2 + 6 ^2 + 22 ^2 = 23 ^2
3 ^2 + 12 ^2 + 24 ^2 = 27 ^2
3 ^2 + 14 ^2 + 18 ^2 = 23 ^2
3 ^2 + 16 ^2 + 24 ^2 = 29 ^2
3 ^2 + 24 ^2 + 28 ^2 = 37 ^2
4 ^2 + 4 ^2 + 7 ^2 = 9 ^2
4 ^2 + 5 ^2 + 20 ^2 = 21 ^2
4 ^2 + 6 ^2 + 12 ^2 = 14 ^2
4 ^2 + 8 ^2 + 8 ^2 = 12 ^2
4 ^2 + 8 ^2 + 19 ^2 = 21 ^2
4 ^2 + 10 ^2 + 28 ^2 = 30 ^2
4 ^2 + 12 ^2 + 18 ^2 = 22 ^2
4 ^2 + 13 ^2 + 16 ^2 = 21 ^2
4 ^2 + 17 ^2 + 28 ^2 = 33 ^2
4 ^2 + 20 ^2 + 22 ^2 = 30 ^2
5 ^2 + 10 ^2 + 10 ^2 = 15 ^2
6 ^2 + 6 ^2 + 7 ^2 = 11 ^2
6 ^2 + 6 ^2 + 17 ^2 = 19 ^2
6 ^2 + 8 ^2 + 24 ^2 = 26 ^2
6 ^2 + 9 ^2 + 18 ^2 = 21 ^2
6 ^2 + 10 ^2 + 15 ^2 = 19 ^2
6 ^2 + 12 ^2 + 12 ^2 = 18 ^2
6 ^2 + 13 ^2 + 18 ^2 = 23 ^2
6 ^2 + 14 ^2 + 27 ^2 = 31 ^2
6 ^2 + 18 ^2 + 27 ^2 = 33 ^2
6 ^2 + 21 ^2 + 22 ^2 = 31 ^2
7 ^2 + 14 ^2 + 14 ^2 = 21 ^2
7 ^2 + 14 ^2 + 22 ^2 = 27 ^2
7 ^2 + 16 ^2 + 28 ^2 = 33 ^2
8 ^2 + 8 ^2 + 14 ^2 = 18 ^2
8 ^2 + 9 ^2 + 12 ^2 = 17 ^2
8 ^2 + 11 ^2 + 16 ^2 = 21 ^2
8 ^2 + 12 ^2 + 24 ^2 = 28 ^2
8 ^2 + 16 ^2 + 16 ^2 = 24 ^2
8 ^2 + 20 ^2 + 25 ^2 = 33 ^2
8 ^2 + 24 ^2 + 27 ^2 = 37 ^2
9 ^2 + 12 ^2 + 20 ^2 = 25 ^2
9 ^2 + 18 ^2 + 18 ^2 = 27 ^2
10 ^2 + 10 ^2 + 23 ^2 = 27 ^2
10 ^2 + 20 ^2 + 20 ^2 = 30 ^2
11 ^2 + 12 ^2 + 24 ^2 = 29 ^2
11 ^2 + 22 ^2 + 22 ^2 = 33 ^2
12 ^2 + 12 ^2 + 14 ^2 = 22 ^2
12 ^2 + 12 ^2 + 21 ^2 = 27 ^2
12 ^2 + 15 ^2 + 16 ^2 = 25 ^2
12 ^2 + 16 ^2 + 21 ^2 = 29 ^2
12 ^2 + 21 ^2 + 28 ^2 = 37 ^2
12 ^2 + 24 ^2 + 24 ^2 = 36 ^2
13 ^2 + 26 ^2 + 26 ^2 = 39 ^2
14 ^2 + 18 ^2 + 21 ^2 = 31 ^2
14 ^2 + 22 ^2 + 29 ^2 = 39 ^2
14 ^2 + 28 ^2 + 28 ^2 = 42 ^2
15 ^2 + 18 ^2 + 26 ^2 = 35 ^2
16 ^2 + 16 ^2 + 28 ^2 = 36 ^2
16 ^2 + 18 ^2 + 24 ^2 = 34 ^2
17 ^2 + 20 ^2 + 20 ^2 = 33 ^2
18 ^2 + 18 ^2 + 21 ^2 = 33 ^2
19 ^2 + 22 ^2 + 26 ^2 = 39 ^2
20 ^2 + 28 ^2 + 29 ^2 = 45 ^2
23 ^2 + 24 ^2 + 24 ^2 = 41 ^2
24 ^2 + 24 ^2 + 28 ^2 = 44 ^2
lol
even Kronecker would like that
Outstanding: clear and easy to understand.
Again, you are awesome. You do a great job not just explaining the process but the reason behind it.
Thanks Asa!
UR MY LIFE SAVER
Thanks for your help may God bless you 🤝
ok , but what if we end up with polynomial expression under integral.
eg
X(t)= 2t
Y(t) = 1+3t^2
Z(t) = 2+ 4t^3
Thank you! Wish my professor taught this as well as you
You're welcome, I'm glad it helped!
Haha funny I was having trouble with this question. This question is from Stewarts Calculus: Early Transcendental!
Thank you very much for this clear explanation. Explained much better than my textbook and professor's lecture combined with one example.
So glad it was helpful! :D
I thought you couldn't integrate a function with its parameter as a bound? i.e. how can t be the upper bound and be part of the function at the same time?
omg youre the BESTTTTTTTT TYSM
thank it help alot i have final in 2 days time. but one quick question what if the end part of the question is change to with respect to arc length measured
from (1,-1,2) in the direction of increasing t ?
thank you !
wow thank you so much!
Thank you very much, Your explanation was so clear and easy to follow (plus the question you solved happens to be the same i was looking at in my textbook).
+alex Laleyan I'm so glad it helped!
wow thnx. i liked this so much i watched it 3 times in a row ha
When you take the integral, doesn't there need to be a + C(vector) that you must calculate for using rvetor=0?
This is a definite integral so we there will not be a +C
:)
Very helpful video
Wow thanks. I didnt know it was this easy the book was confusing
Determine where on the curve given by r ⃗(t)=〈t^2,2t^3,1-t^3 〉 we are after travelling a distance of 20 units. Can someone help with the above question?
Thank you!
You're welcome, Rin! :D
What if the limits are not specified???
What of my integral is a constant?
Remember that the integral (with respect to x) of 3 is 3x, the integral of -7 is -7x, and the integral of k is kx. So integrating a constant just means you need to attach the variable to that constant.
I encountered the exact problem and didn't know how to solve, came here, and found out that it is the exact problem, and even numbers match perfectly....
I'm glad the video helped! :)
Thanks! it really helps a lot for my finals tomorrow. GOD BLESS :D
+Rome Gulay I'm glad I could help. Good luck tomorrow!
omg....your voice is so sweet !!
Thank you for your help! The explanation was very helpful : )
+June Bug You're so welcome! I'm glad I could help!
Some people substitute a dummy variable like "u" when they take the integral. I suspect it's less confusing to evaluate u by plugging in t than plugging in t or t. But the u really threw me the first time I saw it.
I'm confused as to why YT search for Krista's channel of "Chebyshev" gave out this video. I was hoping to get a nice example of how to use Chebyshev substitution. Not that this is not interesting, just unrelated.
Thank u ......may Allah's bless u
tysm :)
This was very helpful! Thank you :)
Glad it could help! :)
Goat
❤
Jesus blesses for u
thank you!
You're welcome, Trevor! :)