Evaluating a Line Integral Along a Straight Line Segment

In this video, I evaluate a line integral along a straight line segment by using a parametric representation of the curve (using a vector representation of the line segment) and integrating.

[kn]

Thank you very very much. You just saved my ass. You got a real talent and ability to get your message across. A very hard skill to have you should feel honored.

Again thank you!

[thomashamiltom]

My teacher felt like just leaving out the equation on how to paramatize! Now it is Thank you!

[oatfarls]

Line integrals always confused me. I'll say that first.

1.) Could you (or someone) possibly explain how the parametrization equation (1-t)r_0 + (t)r_1 works?

2.) How did you know your bounds of integration were from 0 to 1?

3.) Could this problem also be solved using the Fundamental Theorem for Line Integrals you talked about in a separate video?

Any answers are appreciated. I really want to understand this topic. :)

[Zyndraz]

3, 5 years 140 likes and 0 dislikes. You nailed it! This video helped me a lot! Thank you!

[fworeal]

@patrickJMT I am in the EXACT same situation. I knew all the material until we got to this stuff Greens, Stokes, Divergence, Line is really helping. THANKS

[sigalig]

because it is an integral of dx, and x goes from 0 to 1. in parametric form, x is a function of t, so you have 0<t<1

[kenkri]

Please continue to make videos! Way better than my Calc 3 lecturer.

[malleharana]

You are amazing! Keep making videos! You are saving children's lives

[soulreaper]

Thank you so much, I was going crazy over this until I saw your video. I could not understand my book's notion but yours was more understandable. Now's its easy!

[khalid]

i can not smile without you
You're really a myth.
A smile makes us look younger while prayers make us feel stronger and friends? They make us enjoy life forever PATRICK

[StephGover]

*officially in love* love the accent too. totally understand green's theorem and such now, thanks!!

[avneesh]

Why did you take the limit from 0 to 1?

[anamtaj]

i passed three semesters of my calculus only because of u!!!

[datnguyenthanh]

Omg!!. U are my savior, I just totally forgot how to paramatize

[boriecua]

There's no need for me to subscribe because i just search the material that i am learning at the moment. However I subscribed just to support Patrick and the channel.

[mtoldroyd]

Patrick, I'm very grateful for the videos you post. You explain things in a very understandable way, and it's great to work through examples with your guiding steps. I hate to be a stickler, but you're saying "parametize, " (dropping the second R). It's supposed to be "parameterize" or "parametrize" (puh-ram-uh-trize). I had to run a few searches first, to make sure, because I wasn't eager to jump in and challenge the guru of math knowledge!
(Audio at dictionary dawt comm)

[astha]

Why is limit for t is from 0 to 1...I still can't get it ..pls explain

[taylorwentworth]

Because you're evaluating dt and the limits of t are the same as x (because for the parametrization x = t) and if you look at the points, x goes from 0 to 1

[CherylHTheDreamer]

Is there any other way you could have parametrized the line? Or is that equation you used the only way to do it?

[niftyusername]

Thanks! Much clearer than any textbook! :)