❖ 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?

[@PYXyooj]

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

[@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.

[@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!

[@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.

[@austinsears7879]

Why does this seem so simple now but hours of learning/studying make it seem so hard? Thank you so much for putting your videos up, they help A LOT.

[@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

[@Yupyoubetcha]

Patrick you're the best man, I have such a hard time getting everything in class and watching your videos just makes sense of everything. You're essentially my math teacher!

[@blade51192x]

all i can say is thank you for continuing to put these videos up. They are a real help.

[@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]

@tijuanamarisol666 yep, my mistake! : )

[@SuperJAlfa]

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

[@jisookim1606]

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

[@patrickjmt]

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

[@ImTheBowser]

I honestly love you, I so appreciate these lessons. I didn't understand this at all from lectures and now I do. Thank You!

[@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

[@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.

[@elli_onearth]

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

[@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?

[@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 :)

[@MrFarkasOfficial]

oh man whenever i'm in a mathematical doubt i always look for Patrick on the list of youtube vids :) you're a hero, mate, just reminding you ;)

[@judytramvu]

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

[@butson89]

for real, bro. i left that comment this morning cuz i was about to leave for a calculus exam, and i was stressing out, but your videos are such a big help when it comes to studying. Thanks for helping me kick butt today!

[@Alex-ev5mm]

What grade did you get?

[@patrickjmt]

@ian559fresno yep!

[@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!

[@crastatter86]

My calculus teacher actually sends us links to your videos to help us understand the work better if she can't explain it in a way we understand. You are a god-send for us mathematically challenged! Thanks!!

[@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]

@yas72090 glad you like my vids!

[@morganholm449]

back again for calc 2 -___- thanks dude

[@johnvicdulatre5317]

PatrickJMT's examples and explanations are really helpful

[@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.

[@refath522]

My AP CALCULUS AB EXAM is tomorrow and your videos are really helpful and I thank you for that

[@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

[@fiverabbits9049]

Since the Coronavirus hit everywhere, and basically every damn highschooler is doomed to online school, your video *really* helped me. Thank you so much! It's unbelievable how our supposed ministry hired someone and paid him money to tutor us online but I still didn't understand anything from him. I hope I find someone as good as you in Chemistry and Physics too...

[@patrickjmt]

views are way down unfortunately :( glad i could help! i have a few physics videos. check out 'tyler dewitt' for chemistry!

[@patrickjmt]

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

[@Milton21690]

You are awesome! me n my friends are watching this all the way from Costa Rica! thanks, pura vida!!

[@patrickjmt]

@yousif1020 there are other videos...

[@patrickjmt]

no problem, hope the test went well! : )

[@alyssiabuckle3028]

This is great, but i suggest in case you found it difficult to graph those functions, simply subtract them the way you want but put them between absolute values! Thank you Patrick, youre a life saver!

[@patrickjmt]

@warnford areas can not be negative

[@karlracaza7451]

The best video ive toggled so far, thanks mayt!

[@patrickjmt]

@arsmg2009 yes, i do

[@semperfidelis2322]

My calc teacher isnt bad, but i like watching your videos ahead of time to better my understanding, and you are just awesome at teaching

[@Parisx1000]

I Love your videos !! Im a student from england, so ur teaching methods are totally different from what we're taught. Its very interesting !! I'm learning alot. I love americans

[@spitforge8963]

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

[@elliotsavarese]

Exactly what i was looking for right at the start. Bravo

[@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! ):-(

[@RealEverythingComputers]

Thanks for the great video!

[@patrickjmt]

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

[@ab-cm2ic]

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

[@graciegrace6114]

Oh my goodness! Thank you so much! I had no idea what my teacher was doing in class, and now it makes sense!

[@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

[@fadsmfawopefaw]

You're the best!

[@patrickjmt]

@PhxPride1 awwww, i am very flattered! : )

[@HappyBuddhazz99]

@patrickJMT Thank you sooo much for the quick response, I have a test tomorrow. Your videos are extremely helpful, again thanks.

[@indoorfish55]

just droppin by to say THANK YOU, you're the only reason I passed college. Looking back a year after graduating I am so lost lol

[@brco2003]

Great videos. You should do a problem where you need to find the area when the functions stretch above and below the x-axis. Here, you need to set up separate integrals.

[@teezo3afana]

thanks you're better than any teacher i know

[@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.

[@jrmcc173]

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

[@ilovemusic24ful]

I wish you had an example using trig functions. Either way, you rock. Thanks again!

[@mayjandubi1662]

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

[@mkivdubbin]

you have helped me so much in Calc I and II. Thank You!!

[@arizonacardinals94]

Thank u so much, u are way better than my math teacher at school

[@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

[@ninado397]

Thank you! You are the best! So helpful

[@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).

[@cesarrulez2]

Thanks to you, calc 2 is so much clear

[@matthewsanchez3748]

Your the man Patrick, I wish you were my math professor lol. I would recommend using a higher degree of difficulty with examples you pick, just a recommendation to consider.

[@jessi9375]

Yay! I get it now, thanks!

[@patrickjmt]

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

[@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

[@patrickjmt]

glad to help!

[@chymoney1]

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

[@shinybluestar95]

you have honestly just saved me from failing my test. thank you sooo much!!!

[@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)

[@LiveGoodPhilippines888]

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

[@Sparksterfu]

You should get partnered seriously, you deserve some compensation for all your hard work.

[@tomtomtom6924]

i just learned more in ten min than i did in an hour of lecture. thanks man

[@albertolinguini]

Not the best artist in the world, but possibly the best Math teacher.

[@angelheart806]

u're a wonderful teacher Patrick u have just removed the fear of writing calculus quiz in me thanks

[@JoseRodriguez-rm4vw]

Crazy helpful. Thank you.

[@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 :)

[@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

[@Arina-qw3pu]

math final is coming, thank you so much!

[@AshimShunnota]

Like you said in the video , you are not the best artist in the world.But you one of the best who can make math more beautiful for us.Wish you a happy life :)

[@mattg1987]

Man this really helped me understand this. Thanks

[@desmonrock21]

hey patrick, please upload some topic about integration of trigonometric functions.

[@ermitz90]

My coming is exam falls on 22 Nov will all depends on you Patrick..you are my best Sir..

[@hkaur903]

I have a final in 30 minutes, and you just saved my grade!!! Thank You So Much!!!

[@matthattus]

You are a god among men, saving everybody grades out here

[@timephonic]

Sir Patrick you rock !

[@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?

[@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.

[@joycezhang3612]

Thank you so much. Your videos are so clear!!!!

[@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!

[@iKillutch]

Combine the functions, in this case: y=2x, y=x^2-4x 2x=x^2-4x => x^2-6x, and you'll get the points where they intersect, which should then help you identify top & bottom.

[@g23tog19]

your work is good. for the last problem, you couldve have touched on the idea of multiplying it by 2 to minimize the amount of work.

[@jasmineheadlam4629]

Your tutorials are great! Thanks a million :)