Volumes Using Cross Sections - Calculus
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- Опубликовано: 21 авг 2024
- This calculus video tutorial explains how to find the volume of a solid using cross sections perpendicular to the x-axis and y-axis consisting of squares, semicircles, rectangles with height three times the base, equilateral triangles, and isosceles right triangles with hypotenuse on the base of the solid and the leg on the x-y plane. This video contains plenty of examples and practice problems including sketches of the graphs and cross sectional areas for you to master the topic. The solutions are shown including how to evaluate the definite integral in terms of x and y.
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The math is not an issue for me, but the way these problems are worded (and this isn't your fault, or my textbook's) is so hard to visualize.
unfortunately Collegeboard plays dirty that way. Instead of actually testing our skills they only test whether we can read, screwing over all our hard work
yeah i have the same problem feelsbadman
@@picklerick8123 no they are testing if we can apply the concepts to real situations. knowing how to solve the formula is easy, fully understanding the concept is the hard part and solving an equation does not require full knowledge of the concept to solve
@@namechange4103 100% wrong. None of the problems we do in AP exam apply to the real world directly, or at least they do not show up like this.
You won't need to find the volume of a cup in the real world. You will however, use these topic later on in college, and BUILD on them in careers. My point is that they should give more technical problems rather than making horribly worded problems.
@@picklerick8123 i wasnt saying that they apply to real world situations i was saying they apply to real situations based off graphs and tables rather than simply telling you to integrate or derive an equation. anyone can derive and integrate thats easy as hell but the application of derivatives and integrals is the hard part and you have to really know your stuff in order to apply them.
The wording is very simple if you know what you are looking for. they test technical stuff on the Multiple Choice the FrQs are where real men are made.
3:17 Tutor here, just wanted to say thank you for the idea on how to draw this for my students! I've never seen it depicted this way; it's really very sensible
Am really gaining a lot from your tutorials. Thanks a million dear
This is saving me for the calc test I'm gonna have tmrw. Thank u!
after three years did you really get anything form studying
I know full well that nothing is truly saving me from the calc test I have tomorrow, but this video will at least mitigate the damage!
Professor Organic Chemistry Tutor, thank you for an excellent video/lecture on Volumes using Cross Sections in Calculus Two. Volumes of a solid using Cross Sections relies heavily on Geometry. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
Literally the only video that explained this in a way that made any sense of what was happening
you help more than some of my teachers work 👍 you’re great i am going to subscribe
thank you! my textbook explained this HORRIBLY but this clears a lot up
appreciation comment, u have been saving me for the past 5 months in AB calc, thx
I love this man, the only reason I passed math.
Pls face reveal 🥺🥺 u don't know what you do for us you're one of my best teachers and thankyou may God bless you and your loved ones,♥️
This guy's videos always save me
Actual life saver. I was not ready for Calc 2
Our teacher literally explained nothing and gave us a writing project, let me repeat a writing project on this, and he didn't even explain how to do it. Thank you.
You have helped me alot in math bro. And I say thank you for that, keep doing it bro.❤
I can not speak this language. I admire those that can. KUDOS to the smart people of the world.
man im having this in my exam tomorrow , thx so much !
6:55 semi-circles
Thanks for helping me clutch up on my assignment! You are truly an angel ❤
Thanks for the practice problems!
I love you so much Mr. Organic Chemistry Tutor.
Thanks sir.
Wish you will teach other statistical softwares as time goes
I WILL PASS THIS CLASS WITH A GREAT GRADE
THAT’S WHAT I’M PRAYING FOR 😭
@@kiyoshi3002 I passed 😭
@@rpjtv8041with a great grade?
Very helpful video. Thank you so much!
when is the area of the cross section a square and when is it a semicircle? thank you
I know this is probably a late response, but this might help someone else reading the comments in the future, but the shape of the cross sections is almost always provided to you in the question. The only way I can see them not explicitly telling you what shape the cross sections are for a problem like this, is if they give you an image of the solid you are calculating the volume of. From that you could probability figure out the shape of the cross sections. But in the majority of problems, you will be told what the shape is that you should use. Hope this helps!
Great video sir. Thank you
ap calc exam in 7hrs tysm
test in two days guys this one isn’t looking too hot for me😅
thanks for this vid…i’m not gonna fail my quiz now 🤣
Thanq sir..😇
Correct me if I am wrong, but doesn't the formula have a pi in it?
Apologies for the late response, but this may help someone else reading the comments in the future. The formula only includes pi if the cross section is circular. You may have confused the formula in this video with the disk/washer method which does include a pi in its formula. This particular video/tutorial is on volume of solids with cross sections other than a full circle (hence the semi-circle and square cross sections in the examples). So in that case the volume calculation will not include pi. Hope this helps!
happy new year
These are simple problems, the ones on my test are too complex for me.
3:18 the best graphic drawing i have ever seen
thank you so much for saving me bro
Lovin it bro
Got new subscriber
In the first problem how is s equal to y?
You are welcome
He's so smart😧😮😮😮
4:57 I don't understand why it's 8, isn't it 4?
Not 4 , bcz 4 is for whole circle but we r finding of Simi circle. That's why it is divided by 2
2×4 = 8
midterm in an hourrrrr aaaaa
I can't visualize the 3d objects in these examples, it all seems 2d to me :(
these comments are so wholesome
HI IF THEY SAY VANTILATION AIR AT THE FACE OF DEVELOPMENT END MUST BE 0.15M CUBE PER SECOND PER SQUARE HOW DO THEY GET 0.15 ?
Welcome BACK!!!!
Let's go starting calc II off right
3:16. Y are we just assuming that y=s. i dont understand that part
I’m using this for cal 2 and I understood the first one sorta but the second one killed but it’s not your fault I just don’t understand it
Nice
At 2:22 why don't you square the equation before integration?
The square root of x squared just equals x
what software do you use for the board?
I believe he uses Microsoft Paint for these videos.
At 4:42 why did you multiply by two? It's really got me confused.
to get rid of the 1/2. Anytime you have a fraction with 1 as the numerator, you can multiply it by the denominator to get rid of the fraction
Insert surprised Pikachu face*
This yt channel is literally jesus
Me a 7th grader
*Yes*
Trust me if you reveal your face u will hit 10 million subs in very less time.
No! he's not that simple!
Turtle approves of this video
“Holy Jesus. What is that? What the fuck is that?”
you have 3 million subs but still cant monetize your videos? that's pretty bad
@Morgan North yup, it’s kinda sad that he cannot get a better mic even after all his growth. I would imagine he could get a few ads pretty easily.
so many details are left out, jesus. how am i supposed to know how the graph is supposed to look like?
Go back to 7th grade. You can graph it on your own by inputting x values for example or recognizing that the graph indicates a parabola, line, etc. This video was great
I'll be honest. you're videos are super cool and all, but knowing you have been doing this for years and you haven't gotten a nicer mic upsets me a little. its like untapped potential. Engagement in a video has more to do with the audio of the production than the video(within reason) i recommend the MXL 990. its reasonably cheap and you cant top this quality with out reaching diminishing returns in the ratio of price:quality/performance
nah! he's cool like that!
hi madhav
We want some new stuff ...
Wym?? Plus he isn’t youuu servant
I'm going to be honest, this is not your best video