Area Between Curves - Integrating with Respect to y
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- เผยแพร่เมื่อ 7 ก.พ. 2025
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Area Between Curves - Integrating with Respect to y - I show the general formula, graph two functions, and set up the integral in this video.
I calculate the integral in part 2!
For more free math videos, visit PatrickJMT.com
find points of intersection, take a point in-between, use the larger value
Thank you patrick!!! Way back in 2014 when Im taking up differential and integral calculus.. This video saved me. Now Im an engineer all thanks to you and all the videos that you'ved made!! Thank you from the bottom of my heart sir!!
Have an exam tomorrow, and I always come here for my review. Helps so much!
I think that the most difficult part is the sketching graph part. once u draw the right graph, its easy to execute
My final exam is tomorrow and I can safely say that with the help of your amazing videos I think I might actually do well!!!!!!! Thank you PATRICK JMT you are a real MVP
Bro I was 6 when this came out and now I'm watching it for help in my calc II class in college.
I wasnt born yet and im using this for ap calc
i was thinking of taking a tutor but with patrick jmt videos... believe me there is nooooo need. he makes every things clear and simple...thanks
man ... ur the most awesome teacher ever .. i have a midterm in two days and i didn't go to a single class this semester.. I thought i will fail in this subject however, u gave me a hope.. after watching most of ur videos " about 5 hours " i could solve the midterms sample relatively easy .. thank you so much Wish u all the best..
Great video. I always look at your videos before I go to class to set a base for understanding concepts because you very good at explaining in a simplified manner. Thank you.
Your videos are an outline of my book. It's almost like you can made these videos to go along with my class. You are my hero.
you are only looking at the finite region trapped by the two curves. over that small region, 1-y^4 is further to the right
Think about it this way. Which graph lies to the right most. In this case, it would be the graph 1-y^4 because it's the right most when you graph it. Do you mean what I mean? At least at the part where you're determining the area between the curves.
Pattrick you are a really smart man. Thanks for the videos.
Thank you so much for these videos. I would've failed this semester of calc without them---my teacher understands what he's teaching but doesn't seem to understand that he doesn't communicate it clearly (i.e. not explaining steps he didn't write down, not always explaining the strategies to use for solving specific problems, etc.) and the book we have doesn't have enough complicated examples to help with the problems we do for homework and the tests. I feel like you were my actual teacher, lol
You are saving me a lot, thanks to you my last test was pretty high, im hoping it would help too
You are over the moon man,I like your videos big time.
my friend told me that she made a separate account in youtube just to watch your tutorial videos haha..
nice idol patrick! XD this video really helps =)
Thanks for helping me pass everytime we have a quiz!
WOW 1440P....way to go patrick
what..
***** Resolution.
I know.... but it seems pretty clear though.
lol no no....if you watch this video in flash player instead of HTML player...You will see resolution up to 1440P which is essentially 4K...and this is quite rare with videos and is only limited to high end stuff YET....but Patrick's video is appearing in 4K thats why i made that comment
Oh alright man. Sorry I didn't get it at first!
Why did he solve for y=0 to find the points of intersection? As opposed to setting the two equations equal to each other? (Same result I know but unsure why)
Thanks team - pat your a legend
same problem here why did he make x=0 and not x=x so 1-y^4=y^3-y but in that case how could we solve the equation so please if someone can explain
It’s just different ways of doing it... if he did it your way you could equally ask why he didnt do it the other way. Also, his way wiill finds three poinys, the third at 0,0, but if we tried your way we would only get two, where they intersect twice... so his way is a bit more effective in that sense...
thank you SO SO much for these amazing vids. Theyve helped me so much!! just got a 103% on my calc test :)
thanks again~
Thanks for your video. I'm reviewing this stuff and it's helpful. At about 4:05, I think you meant to say "We'll figure out now where x equals 0," rather than "y."
thank you!!!!
patrick you are the BEST
it still helps thans very much for efforts
@Billabong024 the problem stated x = y^3-y.... if its x= then you integrate with respect Y, if its Y= then integrate respect to X.....
Thanks for the video! Great job man, I really appreciate it!
I can smell the Expo marker from here
Patrick JMT... now in stunning HD!
@Jnorrisclay nice grade : ) keep up the good work!
So, can you tell me that when I integrate with respect to x it's almost the same when I integrate with respect to y?
good luck!
Midterm tomorrow, PatrickJMT today :)
How was it?
I admire your work too much teacher.... It's a lot worthy
that's a very good idea. I think I'll start doing that instead of scrambling to watch them the night before a test, haha.
how do you decide which is the left-most or the right-most function? or does it not matter which you subtract from which?
Thank you.
@babicz good luck!!
who thinks that he or she isnt going to pass calculus II :p
66 likes lmao
So did you pass?
I think he did
it seems easy but during the test we cannot solve anything
It really isn’t too bad.. Main things to remember is that you can integrate in respect to Y, most people dont know this. Here for e,g, a y integration makes it easier than X. Sketch graphs for a visual, and then use your formula...
I'm 4 years late but me!
you're left handed like me! :D haha having fun with that whiteboard? Thanks for the help!
many many thanks.
thank you. you explain it very clear but i have problem in drawing the graph.
you're awesome! Very helpful thank you :)
how do you know if you HAVE to integrate with respect to y? I don't quite understand the part when he said chopping the integral apart into two pieces
why is x = 1-y^4 the right most? it seems to me that x = (y^3-y) extends much further to the right than the other function.
how do you find the right most and left most if the fn is slightly more complex and you don't have time to graph it? obviously it's the one that's bigger, but I never learned how to figure that out...
Wow!!! Thanks a lot!! You actually helped me a lot. Just to let you know. :D
how do you know whether to use dy or dx to find the area b/w 2 curves?
I am now expressing my love for you.
THANK YOU!
You can tell they won’t “criss cross” because they’d have to have a third point where they’re equal to each other for that to happen!
6:20 "make sure my graph's not totally crazy." Never did I encounter one single graph in Maths that is not crazy -_-
@MzVixen05 practice practice practice!
Hi! How can I find the intersection when I have been given once function x = y^2 and another function y = 3x-2. I have two functions that are with respect to different variables... What is the method for that?
How would you find the region bounded by y=x**2, the tangent line at (1,1), and the x-axis?
beats me
How did you do in college on calc tests? I feel like I know the material very well but I only get 85s or so because of stupid mistakes because I am nervous when i am taking the tests. Like I can do most things easily but lets say i take the sqroot i forget to make it +/- so i lose points :/
what i didn't get is how to find the points that you gonna subs at the end . when is not given
have you done any video on this subject with trig functions?
How do we figure out which function is greater?
Amith Valentine Set the functions equal to each other and find their intersecting points. Then plug in the x-values for each functions and you'll know which is greater depending on the y values.
Farhan Wasee acurate
make a new function (say h(x)) as difference of the two given functions(say f(x)-g(x)=h(x)) and find sign of the new function(h(x)) to get which of f(x) and g(x) is greater
Thx u
Is it okay if I draw it like f(x) and then rotate it by 90 degrees and call it f(y)?
What is the difference between x=f(y) and f^-1(y)=x?
now there are comments : )
you are amazing
very nice
I'm confused how you got the intersection points of 1 and -1 by setting it equal to 0?
+Diamond Hardman That's exactly right. Plugging in either of those numbers will both equal to Zero.
+Diamond Hardman you have to set each piece = to 0 that will give you. y = 0, y - 1 = 0, and y + 1 = 0. For the second and third equation you would add and 1 to the second equation and subtract 1 from the third equation. Thus, you get +1 and -1.
uhm. Does your technique only work on functions with respect to y (right mots func minus the left most func) ? please give me an answer 'coz we're doing it with respect to x.
Need a 70% for finals on Thursday... hopefully this will do the trick? *fingers crossed some angels start singing after watching this* ('',)
Did you pass?
@@jensmalzer6344 I did! I went on to do an Honours degree and even finished top of my class. Oh how this seemingly little video helped me :D
Thanks. God Bless you
Thanks for the videos, with Khan academy you can speed up the video if you have HTML5, How come I can't do that for any of your videos @PatrickJMT
?
Thanks
Alex
why is the point of intersection +1 and -1 ???
I’m only here because I have a problem that is extremely easy to solve with integration with respect to x, but it requires me to do it also with respect to y, and what’s killing me is I can’t, for the life of me, get the same answers. They should logically be the same since it’s a measure of area, but my area with respect to y is larger by 5.
i dont get how you make the graph. what is the connection of 1/2 in that? 5:18
When we'll use integration with respect to x or y?? I can not understand.
I think the left most point in the function y^3-y would be sqrt(1/3) not -1.
tahnks thanks thanks!!!!!!!
is the answer 8/5?
you rock
I had a pen no function lmfao that made my day!
pen malfunction
Cool, thx:)
thanks my nagga !!!!!!!!
x=g(y) fails the vertical line test
im confused when you do it with respect to x and respect to y
+BubbleCatFTW You just have to examine your graph and figure out which one is easier to do.
why is there no comment?? i like this vid~
i find it confusing since we dont have this lesson (YET)
THANK YOU!!!!
...and it isn't just me either... the other vids work fine.
His pen had a malFUNCTION ... lol
lol right most function, left most function and pen malfunction. :p
you are smarter than the integralcalc krista
Lol, Had a pen malfunction
I dont like the fact that he is left handed
Wtf
Sound on this is messed up... barely audible.
more like how to draw graphs 😒
WHATS THE POINT OF MAKING A VIDEO IF U ARENT EVEN GONNA SOLVE IT???
I never respect it. Y, you ask?