Line integral with respect to x
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- Опубліковано 7 вер 2024
- In this video, as a continuation of my line integral extravaganza, I calculate line integrals of functions with respect to x and y, so integrals of expressions of the form P dx + Q dy. Then I give a very neat geometric interpretation of those kind of line integrals. Enjoy!
Thank you, this really helps me understand the line integral with respect to x and y intuitively.
When you're sitting in calc 1 and the Prof. is boring you to death by talking like 45 minutes about 0 and 1 being the neutral elements of addition and multiplication respectively.
But then the Doc uploads a video with some interesting content.👌
Perfect timing, I was just learning about this!
this is such a good video explaining a important concept which some textbooks don't bother explaining
Thank you so much for this awesome video. I was totally lost with line integral with respecto to x and y. Thanks a lot!
3:25
Really fantastic explaining!
کارت درسته حاج پیمان
I'm a little confused about the drawing at the end. Suppose you pick an orientation of the curve. Then as you traverse the curve one of two things will happen: either the x values increase as the y values decrease, or the x values decrease as the y values increase. Then dx = (dx/dt)dt and dy=(dy/dt)dt will have opposite signs! So the integrals with respect to x and y will have opposite signs.
I think it would be better to give the radius of such a circle or maybe a third point. It could have an arbitrary radius if it weren't centered at the origin
Could you please talk about differential forms some day? That would be really cool!
If only I knew about them!
It's kind of analogous to directional derivatives but for integrals where we define an arbitrary line over which to integrate instead of the coordinate axes
Thanks for the video very helpful
Glad it helped
Muchas graciasss❤
thank you great video
Yes I love this
Thanks so much man
With respect to dr Peyam!
HAHAHAHA, OMG, I get it now 😂😂😂 I thought you meant “Respect, dr Peyam!”
@@drpeyam Lol, meant both!
Dr.Peyam: I really enjoy your channel, as I did this math 25 years ago, and while I don’t currently use it in my profession, I enjoy reviewing it. Is the shadow method an exact method? Reason I ask is I integrated the curve Y=X^2 under the surface of Z=X + 2Y, along the dx interval 0 to 3. My answer was 101.852. I then integrated along the dy interval of 0 to 9 again returning 101.852.
When I used the shadow method, I returned a value of 121...
What am I doing wrong? I’m doing the integration on my TI-84 calculator, so I hope I’m not just entering it wrong.
It’s an exact method, I don’t think you necessarily get the same answer for dx or dy so 121 seems more reasonable
@@drpeyam but it’s the area of the “curtain” of the curve up to the surface. Shouldn’t the answer be the same regardless of the method used? The answer of 121.5 is what I got when I added the two shadows. 101.852 is what I get when just integrating along ds.
@@drpeyam disregard my previous question, I figured out my error....all works out!
Keep you videos coming, great review for us older people who did this long time ago.
Sir, can you please explain to method of multipliers used in solving the partial linear differential eqns. I am confused in it. Please help Sir 🙏🙏🙏🙏.
This is really cool but quite an abstract concept
As a mathematician I don't understand physics lmao.. can relate!
Great presentation. Excuse my ignorance, but I took this subject 25 years ago, so I’m very rusty. I understand that the area on the XZ plane is the shadow of the height Z integrated over dx. But how does the Z value, which is a function of X,Y become only a function of y? In other words ydx.
It doesn’t really become a function of y only. The ydx incorporates both x and y
@@drpeyam but in that case, wouldn’t you need to convert it to x only as you are integrating over X? In other words.....Xdx
i'm confused onto why x(t)=2cos(t) and not 2-2t+cos(t)?
@ 6:25 That should be an extra factor of 1/2 from the Lu Chen, not the Chen Lu.
Papa peyam! :)
3:16
Why are we able to replace dx by (dx/dt)dt in the integral?
Chen Lu! Also that’s the definition of the line integral
@@drpeyam Chen Lu ... Is that a reference to something?
@@stayawayfrommrrogers Chen Lou! Chain Rule! xD
I hope this helps amoung other explations. You can make both side of an equation bigger or less by multipication or division by the same Factor , let say K , on Both Side of Equallity. For xample:
Y= 2X + 5 , is the same as 3Y= 6X+ 15 by applying K=3. Or reduce it by K= 1/10 in which yo are dealing with the same Origional equation, in this case : Y/10 = X/5+1/2. So, it is like you are looking thrugh a magnified glass. The object of concideration stays the same no mater you bring it toward or away from yourself.
Algebra is like a gateway drug, and once you want more you get into single variable calculus, and then you go hardcore and then go into multivariate calculus. Then you decide to go insane and join a complex analysis class, and drop dead in the middle of class both because you can’t understand anything and also because you sniffed hagoromo chalk 😂