❖ Finding Areas Between Curves ❖

[@fuzzygreen3634]

its a great feeling to go from having no clue whats going on in your class to having a solid understanding in under 10 minutes

[@ninako7367]

The same feeling all the time🙇

[@manshisinha7953]

Ikr

[@arulgk9673]

Late response, but it is TRUE

[@mr.noname6109]

You understood it here because you had studied it earlier in the class.

[@Sndbest]

Ya,exhilirtaing experience. On top of all confidence and interest get regained!

[@timhally869]

Now a freshman in college, I have been using these videos to save my ass from failing since 10th grade in high sccool. Thank you sir for 4 years of being the teacher behind the scene that is the reason I pass every math class

[@mikes2fast]

Did you end up graduating?

[@MusicDJz1]

I feel bad because you are awesome, helpful, and I want to donate tons of money to you, but I'm the typical "broke college student" :(

[@TheJellotin]

same

[@silverzero9524]

same

[@aaronhollenbeckakahellfire107]

same

[@Pie128774]

same

[@Updeus]

same

[@patrickjmt]

tell your teacher ' thanks! ' (from me) for recommending my videos

[@ninegames4568]

No one: Every teacher: Sorry for my drawing, I'm not an artist.

[@patrickjmt]

i definitely had people make fun of my drawings in class.

[@ninegames4568]

@@patrickjmt lol, you actually response to me

[@tron433]

I come from 2020. I'm watching a video 11 years ago to learn calculus

[@humnahussain786]

Me also

[@mikes2fast]

I'm from 2021 and I'm here to learn calculus haha

[@patrickjmt]

no problem, hope the test went well! : )

[@AznPandaFTW]

Thanks for telling us the part about it being negative so we got the functions flipped.

[@Napoleon4778]

whatever's the answer, just apply the modulus |-x|... ! :))

[@Specnutz]

Napoleon4778 you know it.

[@amnahassan9647]

I have a test after 3 houres .. i wish i found ur video sooner Wish me luck

[@Flourish12349]

Amna Hassan how was ur test, i hav test tomorrow

[@DieOrBeDead775]

You're asking him how his test was from two years ago lol

[@parhamesmaeily]

LMFAO

[@Flourish12349]

Suvesh Misra i just made a fun comment

[@LeviVillarreal]

How was your test

[@bzboii]

is the answer to the last problem 160/3? EDIT: used a curve calc online and it seems to be 92/3.... EDIT EDIT: whoops found my problem! Now i got it!

[@patrickjmt]

@tijuanamarisol666 yep, my mistake! : )

[@fadsmfawopefaw]

You're the best!

[@morganholm449]

back again for calc 2 -___- thanks dude

[@tgoace]

Wasn't most of this symmetric? Couldn't you just double the integration of one of the small areas and doubled half of the stuff in the middle? For example, integrate the small piece on the right from 2 to 3, and double it. Integrate the positive side of the middle from 0 to 2, and double it. Sum those two results up and that's it?

[@judytramvu]

You are AMAZING. I was so incredibly lost in class. My LORD, I thank you. What a blessing.

[@patrickjmt]

@arsenic222 if you do this, you will not get a negative value, regardless of whether the functions are above or below the x axis.

[@patrickjmt]

@HappyBuddhazz99 set them equal, find points of intersection. take points in between each of the points of intersection, plug them into each function and see which one gives you the larger y value; that is the bigger function.

[@patrickjmt]

@Theheartzofmen to me, the easiest thing to do is to find points of intersection, take a point in-between, plug into each, and find the largest

[@patrickjmt]

@ermitz90 ha! it does not depend on me, i am not taking it! if so, i would rock that test out!

[@xsampsakx]

I just finally have to thank you. You have really helped me to get my engineer diploma, what can I say, but THANK YOU! Great work! Greetings from Finland!

[@patrickjmt]

booooooooooooooooooooooo yaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa!!!!!! glad it helped : )

[@Billy193]

great help! My math teacher actually tells the whole class to watch some of ur videos before lecture so we get a grasp on the math concept before lecture.

[@PYXyooj]

You are seriously a life saver! I did not understand this area stuff, until I watch your videos!

[@patrickjmt]

@solidiquis1 bart simpson is also left handed, if you notice

[@kasrafk8532]

The last one discouraged me

[@patrickjmt]

@ihavetogoful it does feel good, glad i could help :)

[@patrickjmt]

@warnford areas can not be negative

[@patrickjmt]

@WoLGuides you keep up the good work as well! : )

[@patrickjmt]

@yas72090 glad you like my vids!

[@jaronsherwood1501]

Goes in knowing nothing, comes out knowing what the crap this is!

[@lukesanders5310]

As someone who forgot how to even math as of 4 years ago this is a perfect refresher so can't agree more

[@dratsab1980able]

Electrical Eng student from Queens Uni, Belfast told me to make PatrickJMT my new Tutor! (trouble is Im not given the intersection points in my problem, and they dont factorise! ):-(

[@patrickjmt]

i am always lurking around here somewhere

[@jessi9375]

Yay! I get it now, thanks!

[@patrickjmt]

@PhxPride1 awwww, i am very flattered! : )

[@patrickjmt]

@yousif1020 there are other videos...

[@jisookim1606]

im reviewing for ap and i just can't thank you enough right now! you're probably the most helpful guy on youtube :)

[@danielkim5477]

where did you get x=3 and x=-3?, i know u said you have to find those pieces but how did you know it was 3 and -3?

[@patrickjmt]

@resevil787 i am always here!

[@patrickjmt]

or.... the geek at least!

[@brakatsuuu00]

WTF that was easy. my prof taught us using a a small rectangle then you have to find many equation in order to get the dA. to only find out that it have a shortcut. They have the same value. i hope she will check my exam tomorrow using different formula. tnx man!

[@BalkanManic]

Did she give you credit since you used this method?

[@brakatsuuu00]

No she wants to see in my paper what she tought to us. But my second prof doesnt care what method we use.

[@rvbCabooservb]

During 4:56, why did you put x=3, x=-3 when it is x=2, x=-2

[@abdulazizal-amri75]

Why is this too easy here…yet unsolvable in exam

[@patrickjmt]

@ian559fresno yep!

[@lienaejer017]

! Im a mechanical engineering student and now im done in integral / differential calculus with a big help of this man, .you are my best teacher. i aced in our class with the help of this..my grades are very good because of this..thank you very much and keep up the good work!..i will start studying differential equations with this videos this vacation..THANK YOU I SURVIVED WITHOUT BUYING EXPENSIVE BOOKS BECAUSE OF THIS! GOD BLESS 03-26-11

[@mikes2fast]

10 years later, how is everything going? Was mechanical engineering the right path?

[@patrickjmt]

@pepekong awesome :)

[@patrickjmt]

@arsmg2009 yes, i do

[@patrickjmt]

tell them thanks

[@elli_onearth]

Studying right now for my test in Calculus which will start after 40 minutes. Gosh. Thank u so much!

[@mayjandubi1662]

this is excellent. i have finally excelled in maths .Thank you

[@patrickjmt]

yep, glad i could help

[@ginamarie3312]

you saved my life

[@mandisamkhize4475]

Patrick, Patric, Patrick.... #speechless if only you were my lecture

[@ninado397]

Thank you! You are the best! So helpful

[@patrickjmt]

you are welcome :)

[@VishtasticProductions]

I got 92/3 for the last one. 14/3 + 64/3 + 14/3 = 92/3

[@clairevannette4972]

If you're wrong, I'm wrong with you! Got the same thing.

[@brayanzepeda492]

I got 92/3 as well. That's three of us, so we must be correct lol

[@niki-mendozacatalan5903]

2 years later. i do get 92/3 i guess it's four of us know lol

[@youwantchains3dollars211]

If only I could go to where you are now and ask if you could be my personal Math Teacher forever,I would definitely do that BUT IM BROKE AS HELL.

[@patrickjmt]

glad to help!

[@SuperJAlfa]

Dude even my Calculus teacher gives my class your links, that's how effective you are!

[@manshisinha7953]

Oh my god.. thank u so much. I got this !

[@sagarmohan8]

firstly! Thanks a ton ! i hope i write well tomo .... secondly .. pls do make more vids

[@Aggrandize.__]

I got 92/3

[@vontmany]

it should be right

[@Aggrandize.__]

sweet, thanks !

[@josexavier1997]

That's what I got

[@semir2607]

gud job boi

[@Newbport849]

+khanvictt YUSSSSS

[@sweettoothmeryl]

Can someone help me understand things. In the second example, we were already given 2 values of x (X= -3 & x=3). I thought these two values are already our limits of integration. Why then are we equating the two functions to get the points of intersection. I was doing a similar problem in my homework. There were questions in which 2 x values were given and they were automatically the limits of integration. In some weird cases though, the given 2 x values are NOT automatically our limits of integ

[@Virginiaisforskaters]

the area is an uncooked steak

[@KenSchwartzMath]

Another approach if you are allowed a calculator is to integrate the absolute value of the difference between the functions over the entire interval. It doesn't even matter which function you put first, since the absolute value gets rid of the potentially wrong negative sign. That is, integrate |(8-x^2) - (x^2)| OR |(x^2) - (8-x^2)| from -3 to 3. The absolute value makes each negative difference positive. If you are not allowed a calculator, then you have to find points of intersection and write two or more integrals as shown in the video.

[@janindubhanuka545]

Find the area enclosed by f(x)=-x^2+4x+96 , g(x)=-x^3 + 27, x=-1 and x=2 can you please help me find the answer

[@pepekong]

The other day my calculus teacher said "Hey, youtube is a good source for looking at how to solve problems" I was about to say, yeah, there is this Patrick guy who... And before I could speak he said, search for patrickJMT. It was cool.

[@Arina-qw3pu]

math final is coming, thank you so much!

[@obaidaljabry3899]

I tried to find the points of intercept of two parabola y=4-x^2 and y^2=x I failed. I do not know where is my stake. Can I get help please

[@MrVideowatcher7]

I have a question, when i set 2x=x^2-4 to solve for intersection points, i do not obtain the points of intersection you did, am i doing something wrong?

[@HOLYLIFEIFY]

Terrill you had if flip flopped on how you should pursue your college degrees. God spoke while I fellowshiped with him when I was in 2nd grade. Terrill TC!

[@ian559fresno]

Great video Patrick... I have a quick question...if we mix up y1 and y2 will the answer just be negative and all we have to do is multiply it by -1 to get the real answer? Thanks so much

[@jrmcc173]

Well you just saved me from part of my calculus quiz tomorrow. Thank you for existing.

[@omertahagulberk4679]

I can not reach your website. There is a problem that the requested URL was rejected. What should i do ?

[@sazisopoyo21]

How to identify which function is the top and the bottom because some graphs can be confusing to decide which is top

[@cyrusraptor9871]

Hey Patrick , i just wanted you to do me a favor by checking this: u know that area u found in this video between curves (y=2x and y=x^2 -4x) , suppose i wanted to get the volume if this region was rotated about the line x=9 , would the expression be this : volume = 2*pi* integrand ((9-x)(2x-(x^2 - 4x)) lower and upper limite are 0 and 6 irespectively, i did this using ur shell method :) , quick response would be highly appreciated! :D

[@ab-cm2ic]

Never thought a 14 year old video could halp me so much. Thanks man, means a lot to me

[@chymoney1]

this video has 700k views jesus christ. patrick jmt deadass the GOAT.

[@AmaziingNM]

I have a quiz on Integral as Net Change and Areas in a Plane, or Between Curves tomorrow! I can't find any videos about Net Change in your channel, which includes linear motion, the general strategy, consumption over time, net change from data, and work, which deals with Hooke's law. Do you have any of these topics under a different name?

[@sabianhhxevolution]

By taking the anti derivative of 6x-x^2. to take the antiderivative of x^n do [ x^(n+1) ] / (n+1). so to take the antiderivative of 6x-x^2 do [6x^1+1]/(1+1) which simplifies to [6x^2]/2 which further simplifies to 3x^2. use the same method for x^2. if anyone notices i made an error please correct me.

[@arsenic222]

Heya JMT I am kinda confused here.So to find the area bounded by two curves,we integrate the (bigger function - smaller function)?Is there anyway to prove this equation is right bcos i tot we are supposed to take into consideration of cases where parts of graphs are below the x-axis(which gives negative value of area).Thanks

[@njfife14]

@yas72090 Yeah it is very to the point, like both khan and patrick though, I use khan when I know nothing about the subject and Patrick when I know the work but need to figure out what I am doing wrong and just need the points said quickly and clearly. Plus I hate the evil black screen at Khan lol, I feel happier watching Patrick's vids =D

[@carolinerinny2877]

Thank you so much for making these videos! They are so helpful, I honestly could have learned our entire curriculum in a few weeks by watching your vids.

[@AceAites]

@yousif1020 wow...he makes FREE videos for you that are 10x better than Khan Academy and you complain to him about something that is actually KZbin's time/Video limit's fault ? I would be thankful with what I'm given. ;) THANK YOU FOR THIS. It saved me a lot of reading and googling.

[@sheepo023]

why do we need to find the area in the center region? since the center doesn't involve all the 'function' given, i thought we wouldnt need to do so?.. actually what is the concept holding to know which area we are looking for? isit the part that touches all the functions?

[@philmarkpulido8231]

Jeniffer Tenorio Lopez, just chat her. She's beautiful

[@LiveGoodPhilippines888]

Thank u so much sir you're really the very first one whom the explanation i have understood very well.

[@Jojowrryyyy]

YEAH MAN THANK U SOOO MUCH FOR TEACHING US :D.....MY TEACHER IS GOD AWFUL AND YOU ARE A LIFESAVER :D

[@Tribean]

@Kiilex381 No. Since you might have the graphs intersecting each other at different points and/or changing positions as upper or lower functions at certain "x" values. An example of this would be the Trig equations cos(x) and sin(x).

[@mariamA240]

you are the best person in the world it must feel good helping people i just spend 1 hour on this exact question that u did in the video and i was about to give up until u realized i knew you and how great u are thanks man :)

[@rafael1877]

integral of 6x-x^2 is ((6x^2)/2) - ( x^3/3) if you simplify that 3x^2 - x^3/3. then you just plug in the values of 6 (higher limit) and subtract the results after plugging 0 (lower limit)

[@josevela9018]

Uh dumb question but how do you know which is F(x) and which is g(x)

[@spitforge8963]

you make it seem so simple. God bless you!!!

[@zanehawkins3457]

I'm a big fan of Khan Academy, but what I find is that when I come to your videos, I walk away with a good understanding in under 10 minutes> Very well-done explanation! Thank you!

[@thezohan2112]

this is probably a very simple question....but wat if you are given only one curve (say just 4-x^2) and your asked to find the area between it and y=2? btw you're awesome

[@zemoi]

I wish I found your channel earlier into the semester. My teacher is cool, but Caclulus is hard, so. This is a chanel I'll be coming back to for Calc II next semester.

[@patrickjmt]

come back and tell others! social media shares are appreciated :)

[@TheCoolman5500]

waaaw fantastic thank you very much the video is little bit but the next generation will get benefit from you thank you again i wish you full of success

[@KingMald]

To find which function is upper and which is lower, would it not be easier to just input a value for x that is part of both functions and compare the answers?

[@yas72090]

i used to use khan academy which was good but his stuff was too unorthodox and intuition but u teach it like my professor except much more clear, good stuff

[@Theheartzofmen]

Hey can someone please explain to me how you know which graph is the smaller one and which one is the bigger one? can you tell just by looking at the equations?

[@faisalsaleem21]

Wasn't feeling well today. I thought I would watch your video and learn about areas between curves. Got the math mojo going, and feeling better now. Studying for my FET exam.