Line integral example in 3D-space

[jivcho]

that's right t ^(2+1/2) , I am sorry , Not sure how this happened but I got mixed up with the Integration power rule,

Int(x^p)= x^(p+1)/p+1

[jivcho]

Hi there,

Thank you for the great videos. I have one little comment about the solution.

Where you have F(r(t)) =(t^6,-sqrt(2), t^5/2) , shouldn't there be t^3/2 for the z component of the vector field?

Thank you for your time

[DrChrisTisdell]

@jivcho The $z$ component is $2xy$ and along the the curve we have $x = t^2$ and $y = t^{1/2}$. Can you see why you your suggestion is incorrect now?

[hothotcow]

finally! a 3d example!

[MarlosZappa]

What if you have the integral boundaries as vectors? All I can find are examples with scalars as boundaries =(

[jsm666]

IIRC the physical manifestation of this problem is a particle confined on a track, acted upon by a force whose direction and magnitude are not constant from point to point, and the answer determines the magnitude of the work done on the particle by the field (or alternatively the work done moving it along the track against the field's resistance, depending on the sign). Am I remembering correctly?

[DrChrisTisdell]

@jsm666 I could not have put it better!

[prongt]

I loved it, nice :)

More than understandable!

[AryaSravaka]

thanks. with out this video i will miss out 10 marks out of my calculus paper

[DrChrisTisdell]

@AryaSravaka Well done!

[okalov]

Finally, some decent calculus on youtube with an aussie accent! Makes me feel right at home haha thanks for the vids

[DrChrisTisdell]

@okalov :-)

[dailydesi]

u r a cheetah

[akhockey77]

Much more clear than my textbook, which didn't give me any kind of connection to real world applications. Thanks a lot Dr. Tisdell!

[iiiilikeyourcoconuts]

this video was so much more help than my lectures

[hohodsj]

Thanks! very helpful

[madnessdexter]

you rock. im subbing now. 

[tigernov6]

Very understandable explanation. Welldone!

[DrChrisTisdell]

Thanks Tiger!!

[MadMicas]

The explanation is clear and not too fast which is good.

Specifically it would help me if you showed how to paramaterise C in one of your examples because I'm trying to work out how (I don't think you have). I'll work it out eventually. 2019

[DrChrisTisdell]

You're right, MadMicas. In most of my vids on line/path integrals the parametrization is given for the curve of interest.

I'll try to post a video just on how to form parametrizations as it is sometimes an art in itself. (Simple curves like line segments and circles are pretty straightforward though.)

[joycec122]

your videos are really great!

when i did this qn i did a silly mistake but when i looked at the youtube example it showed to me instantly where i got it wrong..

thanks! =)

[DrChrisTisdell]

Good to know that you're enjoying the videos, Joyce. More importantly, I'm happy to know that you are getting some benefit our of them. : )

[obstinate1agitator]

hey man..good job. can u put some examples that r not in our lec notes. and about the 2019 text book u giving out, its so unfair for the regular viewers....may be eventually some random person will win it :(

[DrChrisTisdell]

I will do that for sure, Obst.

Don't worry Obst. You're in the running for the free textbook!