Calculus 3: Triple Integrals (2 of 25) Choosing a Coordinate System: Cartesian

[@ronitmandal7301]

Wow amazed to see a single person knowing about so many different subjects in so much depth. Be it physics or maths or astronomy or chemistry you're really a scholar in each of them! And thanks for your selfless work ✌

[@anjaneyasharma322]

tum hari akkal aur kisise soup nagin nahin woh jo bhi kahan rahe usko verify kar sakte ho ?

[@WHERESSS]

dude is probably a physics professor. I remember one of my physics professors saying that the professors in physics know more math than the math professors. he was the head of the physics department. That sounded crazy to me at the time, but probably has some truth to it

[@wraster07hp36]

@@WHERESSS ı agree in some ways with you.

[@wraster07hp36]

I think too :D

[@rishikatta5846]

Sir your understanding of the concepts and visualisation is truly commendable.

[@michaelkosciewicz1623]

Having now electromagnetism in III semester, I see the necessity to had learned the triple integration in the semester before. But since things were done in hurry me and the other students we were discouraged [2 semestrs condensed in 1] ;( Thank you for your service n' understanding sir Michel! There is somebody on internet to whom I can return n' that's why I follow you :)

[@MichelvanBiezen]

Yes, it is unfortunate that your professors do not go back and show the mathematics needed for electromagnetism. They shouldn't presume that the students remember everything they have seen before.

[@vikrantraghav8930]

thanks michel, u are the best teacher

[@djataberk1]

wish i had time to watch all of your videos but studying with your videos can sometimes become time consuming although they contribute a lot!

[@pfft6119]

why did we not take the limits from 0 to 2 in the x direction at 2:03, what did you mean it would touch the boundary?

[@MichelvanBiezen]

The bottom of the cylinder is a circular disk. Moving from the y-axis to the edge of this circular disk in only equal to "2" along the x-axis, but not anywhere else (it will be less). So you have to find the distance to the edge of the disk which is done using the equation of the circle.

[@WHERESSS]

this brings back memories of my Calc 3 course. it was fun

[@dinamustafa6115]

why did not take the integral of x from -2 to 2 , like y and z , why do we write the limits of integral as equation not numbers as y and z ?

[@MichelvanBiezen]

Because the integration ends at the surface, not at x = 2 or -2.

[@dinamustafa6115]

@@MichelvanBiezen also y ends at the surface? what is the difference ?

[@MichelvanBiezen]

With the first integration, you only want to integrate from zero to the surface. With the second integral you want to integrate from zero to the surface, over the entire range from zero to 2. The second integral sums up all the sums of the first integral.

[@mikepablo]

Hi can you explain integrating the 2nd intergral sq root of 4-y SQ can see how you get 1/2(y sq root 4-y squared + 4 arcsin y/2 (where do you get the arcsin If you could expain please Mike

[@Mornys]

Explaining that takes a lesson of its own. kzbin.info/www/bejne/o3PZq4OlntdjjMk

[@Ivonneselasi]

Is there any video explaining the arc sin ? I'm very confused 😕

[@MichelvanBiezen]

Since sin(30 degrees) = 0.5, then arc sin (0.5) = 30 degrees Or sin (pi/6) = 0.5 then arc sin (0.5) = pi/6

[@vinodensethuraman5475]

How did you integrate √4-y*2

[@MichelvanBiezen]

You can look that up in an integral table, or you can use the trig substitution method (we have a playlist on that).

[@Vaibhav_1996]

Sir ,Using polar for...My ans is coming 32π/3 Plz clarify me

[@MichelvanBiezen]

You can check your answer by calculating the volume of the cylinder ( = area of the base x height = 32 pi)

[@srisaji8895]

Thank you so much. U helped my semester exam 😊😊😊

[@abdisalamadan6599]

i have not understood , where this inverse comr from?

[@MichelvanBiezen]

Sorry, but we don't know which "inverse" you are referring to.

[@kirkpare4116]

it is from the basic forms of integration. You can try to search it and you might as well find arcsec and arctan.

[@YAHOOOOOO5]

why is it x^2 +y^2 =2^2 ? thank you!

[@MichelvanBiezen]

That is the equation of a circle with radius = 2 (the cross section of the cylinder)

[@GOODBOY-vt1cf]

thank you so much!

[@KishoreKannan]

How do you say the height would be 8?

[@MichelvanBiezen]

The height is given in the problem.

[@YAHOOOOOO5]

i think it should be 2arcsin(y/2) rather than 4arcsin(y/2)

[@MichelvanBiezen]

The 1/2 factor was factored out. The video is correct. Thanks for checking.

[@irtizahussain9382]

love ya!!!!

[@talaljs5680]

You are amazingg

[@MichelvanBiezen]

Thank you. Glad you found our videos and you like them. 🙂

[@kacperburczyk8350]

ay ya ya yeee

[@arnelbergosa9575]

❤

[@MichelvanBiezen]

Thank you

[@maddywilliams1945]

I love you Michel

[@ahmedal-ebrashy3691]

You are an inspiration to me. Sir, I have sent you a message on facebook I hope to get some sort of an answer?

[@MichelvanBiezen]

Ahmed, Thank you your message. I don't have time to use my Facebook account, but you can reach me using the comments on the videos.

[@curtpiazza1688]

Cool! 😂