Disc and washer method for volume of revolution (rotated about different axis and lines)

Disc and washer method for the volume of solid of revolution! We will do 6 typical calculus 1 homework problems in this calculus tutorial. Remember the formula for the volume of a disc is pi*r^2*thickness. Here the thickness would be either dx or dy. Definitely draw the graph of the functions to see the area of the region to help you find the volume after the revolution. We will rotate the region about different lines. This calculus tutorial will help you if you are taking calculus 1 or ap calculus AB.
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For shell method, please see 👉 • Shell method for volum...
0:00 y=sqrt(x-1), rotated about the x-axis
1:31 y=x^3, y=x, rotated about the x-axis
5:37 x=y^2, x=2y, rotated about the y-axis
9:58 y=x^2, x=y^2, rotated about y=1
15:11 y=1+sec(x) and y=3, rotated about y=1
22:22 y=x^3, rotated about x=2
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"Just Calculus" is dedicated to helping students who are taking precalculus, AP calculus, GCSE, A-Level, year 12 maths, college calculus, or high school calculus. Topics include functions, limits, indeterminate forms, derivatives, and their applications, integration techniques and their applications, separable differential equations, sequences, series convergence test, power series a lot more. Feel free to leave calculus questions in the comment section and subscribe for future videos 👉 bit.ly/just_calc
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Best wishes to you,
#justcalculus

[@bprpcalculusbasics]

Subscribe for more calculus tutorials 👉 bit.ly/just_calc For shell method, please see 👉 kzbin.info/www/bejne/manNYYKcj7mKe9E

[@beetogarcia9983]

You explained in 25 min what took my professor two weeks to explain. Holy…thank you so much

[@aliavc1404]

I like that you look at the camera and smile for no reason :D Thanks for the video sir.

[@beautyofmay]

whenever i dont understand what he is doing, he looks at the camera and smiles. sometimes that smiles makes me angry. he is a good teacher tho.

[@boredmonke2959]

Understanding the concept behind this is the most important thing. Damn it feels good when you understand everything

[@Antiidfn]

Subtracting one diagram from the other is what really made it click for me, you are the goat!!

[@ryanjw15]

You explained it in less then 30 minutes when it takes teachers and professors 2+ hours to explain this stuff. Outsanding.

[@NIGHT-tj7ks]

This is how a professor is supposed to teach, with joy and clearness. Thank you, this video really helped me better understand the concept of the washer method.

[@bprpcalculusbasics]

Glad it was helpful!

[@cheesehead9980]

i cant put my finger on it but i love the way you teach in this video it’s so clear and focuses on the set up. edit: omg i’m so glad you told me top-bottom=radius, i feel like that clears so much, i didn’t realize it equaled radius.. thank you sm

[@colejohnson141]

You drawing the picture for the last example finally made it make sense in my head. Thank you!

[@bprpcalculusbasics]

😃

[@JCEditzae]

BRO YOUR VIDEO SAVED MY BROTHER AND I'S LIVES THANK YOU SO MUCCCHCHCHCHHCHCHC

[@lesleyy05]

This video made me realize I'm not stupid, I just needed a proper explanation of the set up. Thank You!!

[@Antiidfn]

What an amazing video, thank you for this! You are such a great teacher! Crazy how we're paying thousands of dollars for an education and still end up turning to KZbin!

[@dylanpennington1378]

Lol I have an exam over this at 8am tomorrow morning. Wish me luck!!!

[@bprpcalculusbasics]

Best of luck!

[@lilliampumpernickle4655]

Have one in 45 minutes

[@allengarcia2019]

Does it get better? 😞

[@Eng586]

@@allengarcia2019quite the opposite actually

[@beetogarcia9983]

Same here

[@phlogchamp]

Thanks a lot BPRP! Always appreciate these vids!

[@anthonyholmes8114]

When I was doing a maths preparatory course at university I didn't even attempt a question similar to these because I wasn't confident enough. Thank you for showing me that these types of questions aren't as scary as I thought, and that they're actually quite fun.

[@clueless.2509]

extremely well explained, this covers my whole chapter thank you man! inspirational :)

[@shampoosh]

Thank you!! I've been having such a hard time drawing out the pictures and your explanations and drawings help so much

[@bprpcalculusbasics]

Glad to help 😃

[@nishattasnim5757]

Your videos are really understable,I think my calculus 2 is getting better day by day

[@ardaeser9583]

I watched too many videos about it and you are the best one you solve questions easy to hard thank you

[@KatieandBam]

Thank you so much for explaining. This is very helpful, and I understand the concept so much better now.

[@zoomie9004]

Hi there, I just wanted to take a moment to thank you as I have my calc final tomorrow. This has been really helpful!

[@bprpcalculusbasics]

Best of luck to you : )

[@petereziagor4604]

I'm not going to lie, it's not everything I see in this channel I understand at once but I know they will be super useful to me later once I start calculus properly... Just next year.

[@martincea9100]

Made the concept very clear! Thank you!

[@gabriellabonaretti9320]

Thank you so much! You have such a great way of explaining!

[@Deristrome]

After scourging the internet this is the most comprehensive and time efficient guide that covers everything.

[@claytonvaughters9123]

Excellent video. Thank you very much!

[@basilahmed3000]

thank you so much for this video i really needed someone to explain the 3d stuff to me and now i finally get it. God bless you sir

[@eddiek8950]

You're the best sir watching you from Africa in Zambia 🇿🇲

[@asriel522]

interesting,now find the surface area

[@pa3724]

You are brilliant, thanks for the class.

[@gingermuro6388]

omg you did nearly all the problems of my hw lol I love you

[@averyrose3056]

such a positive and helpful video! i love your concise way of explaining math. will be watching more from you :)

[@bprpcalculusbasics]

Thank you!

[@dr.rahulgupta7573]

Thanks for nice presentation.

[@adityapatel5539]

very helpful video thankyou bro that helped a lot☺

[@professorcrumpets9725]

Literally saved my life!

[@user-pz7dx8ug4f]

this really help me alot thanks

[@johnrine9671]

Very Good! Thank you.

[@qabas_7107]

that was very usefull ,thx :)

[@clintonaschendorff]

this is good and have help me a lot thanks😵

[@StillTenn]

10:00 22:23 don't mind me just listing the ones that really helped me!!

[@mariajulietabaltazar3126]

Thank you so much!!

[@user-pz7dx8ug4f]

Thanks a lot for teaching us about the Disc and washer method and i am only in 6th grade

[@GINGERFIONAIGNACIO]

wow, very informative. thanks for sharing!

[@LORENZOVIACRUCIS]

true! perfect score on the next quiz!

[@petereziagor4604]

Thank you Prof.

[@omograbi]

I have a question: How are we going to integrate and calculate areas if we want to rotate diagonally (around an axis of y=mx+c)? I think it's challenging!

[@KusacUK]

Check Michael Penn’s channel, I think he did one of those last week.

[@bprpcalculusbasics]

Yea he did!

[@jamesss1062]

u r the goat bro tysm

[@_.sebastian]

dude you saved my grade

[@harpleblues]

If I had had blackpenredpen and Mr. Leonard for calculus instructors I would be venturing in a different world right now. They are individually and collectively the best I have ever seen!

[@twokidsmovies]

Thanks!

[@hatembahri4314]

you are the best thank's a lot

[@zplus11]

Very helpful... thanks

[@MohdAyan-pq5sy]

You be my dream teacher.

[@-GouthamKumar]

Thank you bro

[@akankshyadas9759]

Thank you for saving my brain getting lost in space..❤

[@user-ir4hz8up7g]

hi. is there any way you could do a video about rotating around an angled line eg y=x. if not what are some good reasorcces to properly understand this concept

[@sidspegasus]

For question 3 , shouldn't it be y^2 - 2y and not the other way round? Because the curve is above the line?

[@lilliampumpernickle4655]

That’s what I was thinking

[@Eyelidyoinker]

@@lilliampumpernickle4655 Probably too late to answer this but its because of the distance from the axis of rotation the y axis in this case.

[@nujim]

@@Eyelidyoinker It's never too late. I had the exact same question and I can't seem to find a reasoning why until now. This makes sense and thank you for your explanation :)

[@stryky3152]

lmao what are the chances i see this video when I just did a lesson on volumes of solids of revolution today. thanks so much for the video

[@noahanderson8688]

Lmao me too I think his calc 2 class must be doing the same units

[@emmettforrestel1071]

Thank you

[@CarRevvedGaming]

at the last one you can use the shell method using the dx, which I find easier

[@harpleblues]

I’d like to see the solution to a problem like this - suppose a commercial artist designs a bottle (for example a Coke bottle) and corporate passes the bottle off to you and requests that you dimension the bottle to hold 12 ounces while preserving the exact shape. How would you do that using calculus? Then I’d like to know how this is done for an asymmetric bottle. I’ve been wondering how this is done for years.

[@brucelam115]

10:51

[@di-riso]

At minute 15 i decided to get everything in terms of x and got the same answer(just in the y world),if i would do that on a test would it be considered wrong?

[@wolflexz]

How do you know which function goes first?

[@jaidybanaag918]

Sir, how about comparing the shell method and disk method, does the two having a same results?

[@paulmaingi7382]

Question: why do we use dL (dL²=dy²+dy²) for surface of revolution integration but only dy or dx with no slant for volume?

[@two697]

That's a good question

[@eduardvalentin830]

In what areas are these used?

[@pikachudemsy9751]

Could you do a the surface area

[@alexemnn]

How you get 1,5 for the first problem?

[@edungdivinefavour6977]

Wow,.. Just wow

[@opufy]

My test is in 1.5 hours :D

[@dustinkim303]

GOAT

[@DanielW607]

lol this sounds an awful lot like physics

[@bossinfinite9742]

Me still thinking In fast! He has big beard but in just calculus he is clean why?

[@TheJJ65]

These are old videos

[@bread3088]

20 minutes…..

[@yt_pointless]

Bro will you marry me

[@pranshugautam8890]

Buy a proper Mike dont carry Mike in hand.

[@andrej8875]

Buying people is illegal

[@ImperialAssassi4U]

I'm a bit confused - with the second example, the integral is set up as x^3/3 - x^7/7. This makes sense because the line y=x is bigger than the line y=x^3. However, right for the next example, you do the opposite. Why is this? When I worked on it myself I did (y^3 - 2y) as the set up of the integral but it is wrong. Can someone explain to me why?