Awesome breaking news! Patrick JMT just won all six of the available Nobel prizes today. He won the Nobel prize in peace for saving thousands of emotionally distressed students from murdering their worthless professors on the night before their terrifying failed exams. He won the Nobel prize in economics for helping thousands of students save tons of money by aiding them for free with the math problems their professors were unable to explain in English. He won the Nobel prize in medicine for saving thousands of students millions of dollars in medical bills (and many days of wasted time in the ICU at the local hospital) due to stress and frustration-related illnesses brought on by horrifying math classes. He won the Nobel prize in Chemistry for saving thousands of students from drinking concoctions of deadly poison on the nights before their dreaded failed exams. He won the Nobel prize in Physics for saving thousands of students from jumping off cliffs in depression over their horrible grades and future certainty of getting straight Fs in Calculus class. Finally, he won the Nobel prize in literature for turning students who otherwise would have had nothing to offer the listening world but angry grunts and senseless mutterings (due to their extreme anguish of heart over the certainty of failing all future Calculus exams---along with murderous death threats against their professors who don't have a clue how to speak English or how teach math) into cheerful, verbose, eloquent proclaimers of the praises of Mr. Nobel Prize Patrick---as seen in this comment and those below. As if that wasn't enough to constitute a "good day" for good Mr. Patrick JMT, the International Mathematical Union decided just today to declare Nobel Prize Patrick "the Greatest Mathematician on the Face of Planet Earth" and second only in historical greatness to Sir Isaac Newton himself, the inventor of the subject Patrick so faithfully teaches to mankind. For his saving millions of students from suicide, stress-related illnesses, untimely death, and murder, and for his successful efforts in enriching the lives of so many other millions, let us now officially hail PatrickJMT as Global Emperor of Mathematical Altruism! Hoorah!!!
PLEASE put more examples up! ones that have equilateral triangles, semicicles, and isosceles right triangles! you would be a complete lifesaver:) thank you patrick for showing me how to do this one though, i understand it completely after i watched this video:D
Hey Patrick, I thought this video was great. However, I would suggest linking all the cross section videos under an auto-playlist so that they would be more navigable. Might I also suggest an Ex 2 comprising of how to do this when a simple function (say y = 1-x) is bordered by some axes and then has cross section perpendicular to the y axis. I am confused as to how the cross sections perp. to the y axis changes the integral expression. Thanks again!
Hey Patrick, can you make more versions of volumes using cross sectional slices like this one? Please thanks. This was very helpful. Thank you for your hard work and dedication.
I think you do a great job with these math videos. I'd like to request a couple more videos explaining cross sectional slices. Where the slices are different shapes.
@sjsawyer Discriminant and both roots formulas are quite necessary sometimes, when, for example, you need to find something with respect of parameter of a variable. And the factoring method that patrick is using only works when the roots (x1 and x2) are rational numbers. When they are not, you won't get out without the harder way.
There is one slight yet major difference. Finding the volume requires you to square the given slices. Notice that when you find the area under a curve, you don't square the slices.
Great video thanks so much. Could you please make a video on net change vs total change. Its when you integrate v and then either subtract or add two integrals.
im really confused when it comes to drawing the actual cross sections. What does it mean when a shape is perpendicular to the x axis, or parallel to the y axis, etc. I dont know how to draw them...
I have to find 24 individual equilateral triangle cross sections i already have the theoretical volume. Do i just change the intervals on the integrated equation?
patrick, I don'T get it; if its a surface then the square is out; if its a volume, something like pi is missing (I think). By the way how would you calculate the surface of this bowl??
@exscape Thanks. Though they teach us in schools to first find the discriminant, then x1 and x2, and then write it as ax^2 + bx + c = a(x - x1)(x - x2)
@Gytax0 Of course, you can rewrite any parabola in that form (so long as you include complex numbers), but if you can factor it with rational roots then there are techniques which make doing so much faster than using the quadratic formula to find the roots and rewrite it in the form y = a(x-x1)(x-x2). I am of course talking about nice theoretical models. In the real world, your equations will probably not be so pretty.
@Gytax0 You can do it in your head quite easily if you know how. Since I can't link here, google (without quotes) "purplemath factoring quadratics". In short, it's +3 and -1 because you need two numbers that multiply together to -3 (... 2x -3) and add together to 2 (... + 2x).
+Carter Rogers for me, the question is why is he using a square at all instead of a rectangle which is base * height. Like (f(x)-g(x))dx. Why use square when it creates so much more arithmetic?
+Stephanie Munoz i still don't understand why he squared it. if finding the area between two curves is the integral of a to b . of f(x) - g (x) dx. it says so in my textbook
+redwing644 redwing, he is not just finding the area between two curves. in this problem he is finding the volume of a solid bounded by 2 curves where the cross sections are perfect squares. so first you must find a generic formula for the area of the cross section, which for a square is just the length squared. to get the length, you find the distance between the curves, which in this case is just the top function minus the bottom function. so the solution is the integral from a to b of ((top function - bottom function) squared)
You kidding me? You give one example over 10:43 AND it requires a calculator? We'd much rather see two or three examples where you don't simplify, or have manageable numbers.
Awesome breaking news! Patrick JMT just won all six of the available Nobel prizes today.
He won the Nobel prize in peace for saving thousands of emotionally distressed students from murdering their worthless professors on the night before their terrifying failed exams.
He won the Nobel prize in economics for helping thousands of students save tons of money by aiding them for free with the math problems their professors were unable to explain in English.
He won the Nobel prize in medicine for saving thousands of students millions of dollars in medical bills (and many days of wasted time in the ICU at the local hospital) due to stress and frustration-related illnesses brought on by horrifying math classes.
He won the Nobel prize in Chemistry for saving thousands of students from drinking concoctions of deadly poison on the nights before their dreaded failed exams.
He won the Nobel prize in Physics for saving thousands of students from jumping off cliffs in depression over their horrible grades and future certainty of getting straight Fs in Calculus class.
Finally, he won the Nobel prize in literature for turning students who otherwise would have had nothing to offer the listening world but angry grunts and senseless mutterings (due to their extreme anguish of heart over the certainty of failing all future Calculus exams---along with murderous death threats against their professors who don't have a clue how to speak English or how teach math) into cheerful, verbose, eloquent proclaimers of the praises of Mr. Nobel Prize Patrick---as seen in this comment and those below.
As if that wasn't enough to constitute a "good day" for good Mr. Patrick JMT, the International Mathematical Union decided just today to declare Nobel Prize Patrick "the Greatest Mathematician on the Face of Planet Earth" and second only in historical greatness to Sir Isaac Newton himself, the inventor of the subject Patrick so faithfully teaches to mankind.
For his saving millions of students from suicide, stress-related illnesses, untimely death, and murder, and for his successful efforts in enriching the lives of so many other millions, let us now officially hail PatrickJMT as Global Emperor of Mathematical Altruism! Hoorah!!!
Please do more example videos on cross-sectional slices they seem to be a major part of my Calculus II course in college.
+M Alc Agreed
You are a lifesaver, my teacher isn't bad at teaching but its just so much easier to figure it out when its laid out like this
Mr Patrick, I don't know how I can express how helpful these video were to me. Your video started to help me since I was in basic math. THANK YOU SIR.
Thanks Patrick - keep up the great work! I’m a third year subscriber, and still think this is one of the best math-tutoring channels out there...
PLEASE put more examples up! ones that have equilateral triangles, semicicles, and isosceles right triangles! you would be a complete lifesaver:) thank you patrick for showing me how to do this one though, i understand it completely after i watched this video:D
thank you so much, this was killing me. I had no idea what it was even asking until now.
Have a calc test on this tomorrow, and my understanding was scarce. Thank you so much for the tutorial.
This was a tricky concept for me, but your vid cleared it up, thank you so much.
Dude, my doctor at University told us to check your vids on youtube. you are a freakin boss.
Hey Patrick,
I thought this video was great. However, I would suggest linking all the cross section videos under an auto-playlist so that they would be more navigable. Might I also suggest an Ex 2 comprising of how to do this when a simple function (say y = 1-x) is bordered by some axes and then has cross section perpendicular to the y axis. I am confused as to how the cross sections perp. to the y axis changes the integral expression. Thanks again!
you're a wizard. not that my calc teacher is bad, but I had no clue what was going on. you saved me...
Hey Patrick, can you make more versions of volumes using cross sectional slices like this one? Please thanks. This was very helpful. Thank you for your hard work and dedication.
I think you do a great job with these math videos. I'd like to request a couple more videos explaining cross sectional slices. Where the slices are different shapes.
@sjsawyer Discriminant and both roots formulas are quite necessary sometimes, when, for example, you need to find something with respect of parameter of a variable. And the factoring method that patrick is using only works when the roots (x1 and x2) are rational numbers. When they are not, you won't get out without the harder way.
Thanks a whole lot!
Explained a lot of reasonings for the "generic formula"
got a an A+ on my math test today...THANKS TO YOU!!!!!!!!!
you r actually the reason im gonna do ok in the exam :D
much love keep up the amazing vids thanks a ton
Isn't this essentially the same thing as finding areas between curves
There is one slight yet major difference. Finding the volume requires you to square the given slices. Notice that when you find the area under a curve, you don't square the slices.
good luck :) study hard!
Great video thanks so much. Could you please make a video on net change vs total change. Its when you integrate v and then either subtract or add two integrals.
This is so incredibly helpful. Thank you for helping me pass calculus :)
i'd really appreciate it if you put up more examples! :)
@twotall2fall to find the area of a square
At 1:16 how did you know that it factors as (x + 3)(x - 1) and not as (x - 3)(x + 1)? Or did you do the algebra in your head?
Do you think you can do a video with cross sections where the base is defined parametrically?
is there an easier way to integrate the equation such as a u-sub or do you have to do this foil out method?
im really confused when it comes to drawing the actual cross sections. What does it mean when a shape is perpendicular to the x axis, or parallel to the y axis, etc. I dont know how to draw them...
He makes it look so easy
I have to find 24 individual equilateral triangle cross sections i already have the theoretical volume. Do i just change the intervals on the integrated equation?
patrick, I don'T get it; if its a surface then the square is out; if its a volume, something like pi is missing (I think). By the way how would you calculate the surface of this bowl??
calculus 2 is my last math course Im so happy
Should volume be multiplied by pi?
@Gytax0 He knows that x=1 is a solution to the equation, thus (x-1) is a factor.
Amazing! Thanks for the great vid! Helped a lot!
Awesome! Thanks sooooo much! Great video!
anymore examples?
You are a genius
@exscape Thanks. Though they teach us in schools to first find the discriminant, then x1 and x2, and then write it as ax^2 + bx + c = a(x - x1)(x - x2)
"The uploader has not made this video available in your country." What the heck man!
Is there something wrong with the volume?
what about semi circles?
@Gytax0 Of course, you can rewrite any parabola in that form (so long as you include complex numbers), but if you can factor it with rational roots then there are techniques which make doing so much faster than using the quadratic formula to find the roots and rewrite it in the form y = a(x-x1)(x-x2). I am of course talking about nice theoretical models. In the real world, your equations will probably not be so pretty.
@Gytax0 You can do it in your head quite easily if you know how. Since I can't link here, google (without quotes) "purplemath factoring quadratics". In short, it's +3 and -1 because you need two numbers that multiply together to -3 (... 2x -3) and add together to 2 (... + 2x).
wow......thanks again....what do u do for a living?
Can you make a video like this using semi-circles and triangles? :D
Awesome tutorial, thanks
Thank you so much for the help.
does anyone know the reason why you square the function? It's just not clear to me what that implies in the computation of the volume
Area of a square is side^2. Your side is f(x) - g(x). Thus, you get (f(x) - g(x))^2.
Carter Rogers how do you know which equation is f(x) and which one is g(x)?
bclai7 you do equation on top - equation on bottom.
bclai7 you have to know how each basic funtion is shaped (polynomial, radical, etc) then determine which is which from there
+Carter Rogers for me, the question is why is he using a square at all instead of a rectangle which is base * height. Like (f(x)-g(x))dx. Why use square when it creates so much more arithmetic?
Can i know why u dont put in "pie" ?
Is this volume or area?
Thank you!!! Hallelujah
@sgtcojonez The integral of A(x)dx is the volume from a to b ;)
At 3:40 why would you square that?
ok thanks!
+Stephanie Munoz i still don't understand why he squared it. if finding the area between two curves is the integral of a to b . of f(x) - g (x) dx. it says so in my textbook
+redwing644 redwing, he is not just finding the area between two curves. in this problem he is finding the volume of a solid bounded by 2 curves where the cross sections are perfect squares. so first you must find a generic formula for the area of the cross section, which for a square is just the length squared. to get the length, you find the distance between the curves, which in this case is just the top function minus the bottom function.
so the solution is the integral from a to b of ((top function - bottom function) squared)
GOD BLESS YOU!!!
More slicing method? Why is there no tutorial no slicing method?
g e n e r i c
Patrickjmt just pulled out a calculator. SHIT just got serious.
How do you know that it's a square? I understand everything except for that.
I know i'm a bit lit on the reply but the question will tell you what shape it is.
lol a bit? its been 6 years
@Gytax0 whattt?? that sounds more complicated than necessary
Couldn't you have used a reverse chain rule? Instead of breaking apart the equation
I would love for you to my lecturer :')
**squares with diagonals in the xy-plane**
you > my doctor at university
thanks so much!
I love how you're left handed. It hardly gets in the way. ^^
Also.... You forgot your cubic units
Thank you!!
they could've made the name less intimidating hahah. whatcha studyin there, bud? 'the slicing method for calc2.' "..ohh wow, ok. well, goodluck :\"
nice
cool beans
@sgtcojonez NVM sorry
I was confused for a sec.
So it's the integral of the area? gg i got the semicircle one wrong
Patrick u should have an advanced scientific calculator lol
"generic"
@katerinawsy the problem will tell you
You kidding me? You give one example over 10:43 AND it requires a calculator? We'd much rather see two or three examples where you don't simplify, or have manageable numbers.