Finding the Area Between Two Curves by Integration

Рет қаралды 484,785

Күн бұрын

By now we are very familiar with the concept of evaluating definite integrals to find the area under a curve. But this always gives us the area between a curve and the x-axis. Is there some other way to apply integration to find some different area? Yes there is! We can also find the area between any two curves on the coordinate plane over some interval, simply by subtracting two integrals. It's easier than you think! Let's find the area between two curves.
Watch the whole Calculus playlist: bit.ly/ProfDaveCalculus
Watch the whole Mathematics playlist: bit.ly/ProfDaveMath
Classical Physics Tutorials: bit.ly/ProfDavePhysics1
Modern Physics Tutorials: bit.ly/ProfDavePhysics2
General Chemistry Tutorials: bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: bit.ly/ProfDaveBiochem
Biology Tutorials: bit.ly/ProfDaveBio
EMAIL► ProfessorDaveExplains@gmail.com
PATREON► / professordaveexplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: amzn.to/2HtNpVH
Bookshop: bit.ly/39cKADM
Barnes and Noble: bit.ly/3pUjmrn
Book Depository: bit.ly/3aOVDlT

Пікірлер: 110

@minusart5242 2 жыл бұрын

Spent an hour long lesson on this and didnt understand it at all, went home, watched a 10 minute long video and understood it completely. Thanks so much!

@ghost0861 Жыл бұрын

The beauty of math youtubers

@ramunasstulga8264 11 ай бұрын

An hour long lesson tells exactly the same thing

@gam7880 9 ай бұрын

@@ramunasstulga8264 the explanation on lections is sort of more complex i think..

@goratron1 9 ай бұрын

That is math unfortunately.

@hellboy4167 7 ай бұрын

Yes it works after 2years!

@nowsherwankhan3834 3 жыл бұрын

man u explain 1 1 hour lecture with animations in 10 minutes - this is amazing!!! thank u!

@ranjani634 2 жыл бұрын

Damn true😂

@gentleman4844 2 жыл бұрын

True dat

@user-mq8qu4cx1f 2 ай бұрын

i dont like manchester united

@user-hv6ef9ie1g 3 ай бұрын

OH MY.. AN HOUR LESSON OF THIS AT MY UNI DIDN'T MADE ME UNDERSTAND A SINGLE BIT. BUT A 7 MINUTE VIDEO ON KZfaq DOES. THANKS DAVE!

@CusPedro 3 жыл бұрын

I'm learning this subject on my own. The first one of these problems I had to solve was with sin x and cos x. I guess no one wanted to explain it in detail so I took it upon myself to watch the same process with simpler inputs and to my surprise, it allowed me to do the similar problem with trig identities. I thank you very much.

@jasperjohnson83 3 жыл бұрын

Thank you, professor Dave. Your way of explaining is sooooo sweet. Please keep it up. You've helped me today

@alejandroalmarza8447 2 жыл бұрын

Excellent explanation….clear as water and better than any of my College PhD professors…keep the great work.

@aumpatel6571 3 жыл бұрын

Finally, youtube algorithm does help. This is gonna be a huge help in my oct/nov 2020 as exam.

@samisiddiqi5411 3 жыл бұрын

How'd it go?

@teriiyaki_god 6 жыл бұрын

such a shame i had my add math exam 2 days ago this would have helped

@akelashirozaki 3 жыл бұрын

Malaysian bro?

@robertlind6255 2 жыл бұрын

great video! explained clearly and precisely!

@jonatanberge94 10 ай бұрын

In 7 minutes you explained this better than my professor did in 2 hours! Thank you:)

@sadmanjahan1442 2 жыл бұрын

That was very helping I was confused about this matter for a time that was easy to understand in a quite short time thanks

@haterusakasa5118 Жыл бұрын

yes! Thank you for making this video I didn't understand at first but I 'can catch up thanks to you. you're my hero for this lesson

@kenrickmukaya2481 2 жыл бұрын

Your explanation is just amazing Thank you

@vunguyen2246 5 жыл бұрын

Love your lessons from Vietnam.

@sadlerpapua9118 10 ай бұрын

You make it seem so easy. Thank you sir🎉

@deankhan580 2 жыл бұрын

This gives me more knowledge than my two hour lectures. Thank you so much

@musawaleed224 3 жыл бұрын

Excellent explanation thanks very much

@SamanthaSmith-bf7ub 2 жыл бұрын

I appreciate you Professor Dave.

@waffle_chris2 3 жыл бұрын

Thanks for the help!

@MrMarkgyuro 4 жыл бұрын

thanks professor!!

@citizenofreality2751 2 жыл бұрын

Very well done!!

@drumpfbad5258 4 жыл бұрын

I'm a sophomore in Algebra 2/Trig, I'm going into Calculus BC next year and I've been watching your videos to help me prepare for next year. They're pretty helpful and especially the practice problem at the end. Keep up the good work!

@patrickyang3157 4 жыл бұрын

Dont you still have to take Pre calc and Calc AB?

@drumpfbad5258 4 жыл бұрын

@@patrickyang3157 Why would my school require me to take calculus AB and BC? That's like requiring you to take Chemistry before Chem Honors if you just wanted to take Honors. It's an accelerated version. You should be asking if I was forced to take normal Alg 2 last year. And no, I don't need to take precalc, as long as I meet the credit requirements for math (Which I already did last year actually), we're all good.

@TheIvinMKoshy 6 ай бұрын

Dude, that analogy at the beginning made it all click together, ty sm

@kawanganyirenda452 9 ай бұрын

wow !!! I will face my Exam with confidence and boldness on 30 th this month knowing that I will have information. Thank you Professor Dave

@vaigarainila 9 ай бұрын

very nice video. Thank u, sir

@jakebrowning2373 5 жыл бұрын

If the interval extended beyond the intersection of the graphs, would you have to split up the interval so you wouldn't get negative area?

@drumpfbad5258 4 жыл бұрын

If you calculated an interval that goes past the intersections you did something wrong...

@xy6762 Жыл бұрын

Thanks man i got a test tomorrow this will definitely help me

@Thaumius 6 жыл бұрын

if you were to find the area enclosed between x^3+5 and x^2 it would be annoying to sketch. Note sometimes the function can change from a certain interval is the top function.

@muhammadrafiq8203 2 жыл бұрын

Sir i m from Pakistan . May i am wrong but i try a lot of time on compression question , so i got different answers sir.

@Ok.9. Ай бұрын

Thank you bro, I have my calc exam tomorrow, this will greatly help.

@SurinderKumar-os5il 4 ай бұрын

Excellent sir

@shrimp6778 Ай бұрын

In 7 minutes you explained better than my teacher's 2 hours lecture 🫡 Thanks man

@lusianelundu2702 11 ай бұрын

Thank you sir❤😊😊😊

@jamka5 Жыл бұрын

this guy goated fr 🔥💯💰

@LaraSchilling 6 жыл бұрын

I'm slightly excited that I managed to do this kind of problem today quicker than my tutor haha! Hashtag things that happen when you're learning calculus for the first time at the age of 30.

@uggo2488 4 жыл бұрын

idk you but that sounds freaking awesome and i'm so proud of you!!!

@LaraSchilling 4 жыл бұрын

@@uggo2488 Thank you! I haven't done any calc in 2 years, so I've forgotten everything xD In one ear, out the other.

@silentintegrals9104 3 жыл бұрын

Great Lara!

@ThOtherzz_ 5 ай бұрын

What if the intervals are not given? How can you determine the intervals of each function and find its area?

@ThOtherzz_ 5 ай бұрын

The only given are just two functions e.g. f(x) and g(x) and you're only to find the area bounded by the two curves. Example: Find the area in the plane bounded by the curves y = x-1 and (y-1)^2 = 4(x+1)

@ProfessorDaveExplains 5 ай бұрын

You can find the boundaries by setting the functions equal to each other to find where they intersect.

@julianarens3908 2 жыл бұрын

big help!

@vikashgangatharan6118 3 жыл бұрын

Excellent 👍

@manfredman5075 2 жыл бұрын

I love this stuff!

@grattitudetebogo9501 9 ай бұрын

Beautiful man

@yazeedalshammari3838 5 ай бұрын

yep the problem is me, ive seen around 20 vids and couldnt understand a single one.

@HarpSeal Жыл бұрын

For 4:05, If we were to be given two functions to integrate, how do we know which function comes first in subtraction without graphing?

@khon Ай бұрын

First try it and if you get a negative answer that means that we substracted small one from big one (because a area can not be negative) then try it again or make it a absolute value

@yaasioncabdisamed335 3 жыл бұрын

Pro, give me advice because I never understood Physics and Math. What I do

@egreeno Жыл бұрын

What does the "dx" mean?

@user-oj4tj8li4g 9 ай бұрын

Hello professor Dave, please how do you know which of the functions is the upper function and which is the lower function.

@arbaj03 8 ай бұрын

You can just draw it to understand right

@ericyow6265 11 ай бұрын

can someone help pls.. what does it mean when i integrate a function with (a,b for eg) i get 0

@user-kd5sn9zx9h Жыл бұрын

thanks you for teaching me math jared leto

@jacobvarghese4722 11 ай бұрын

Bro made this easy to understand

@DarpaSeven 2 жыл бұрын

Best ❤❤❤

@Versatile_Voyage 3 жыл бұрын

Is this with the use of definite integral?

@adanernestochavez1423 2 жыл бұрын

yes, at the end you should get a number and not +c

@sharirhariparsad5777 Жыл бұрын

dude that square donut example is gold

@JoylessBurrito Жыл бұрын

What if you're finding the area between 2 curves and the bottom curve dips below the x-axis? Do you have to change your equation at all, or does it all just even itself out?

@tommyswag69 Жыл бұрын

I'm probably way too late but it'll even itself out, the logic works the same way

@JoylessBurrito Жыл бұрын

@@tommyswag69 thanks

@jvg6877 Жыл бұрын

When i tried doing the comprehension check I tried graphing out both functions in my calculator and they don't even make an area they are in completely different spots, am I doing something wrong? I stared at them many times and I'm sure I typed it in correctly

@prismoandfriends 6 ай бұрын

wow, I really did understand

@user-kh8fj6ln3z 10 ай бұрын

Wooow I love it

@truNam143 3 жыл бұрын

Love❤️from India 🥀🥀🥀

@user-us6db8ws8y 6 ай бұрын

Let me remined you sth DAVE you are smart.

@halieberry9935 2 жыл бұрын

I can confused where did you get x3/3?

@carultch 2 жыл бұрын

From the power rule. For differentiation, the derivative of x^n is n*x^(n-1). For integration, the indefinite integral of x^n is 1/(n+1) * x^(n+1) + C, as long as n does not equal -1. Set n=2, and you'll see that n+1 = 3, and thus the integral of x^2 is 1/3*x^3 + C. When n=-1, ln(|x|) + C is the indefinite integral.

@mohamadabdullah5517 3 жыл бұрын

geogabra ?

@shimba8455 2 жыл бұрын

I love you

@srinivasaraodhulipala3542 4 жыл бұрын

👌👌👌

@herseycokanlamsiz 2 жыл бұрын

thought i was stupid until watching this. acing maths tests now go brr

@Doziano Жыл бұрын

DAVE YOU FUCKIN GENIUS!!! THANK YOU

@coolguy1873 Жыл бұрын

last two functions dont overlap?

@dominicmarinduque848 28 күн бұрын

yes bro ive been trying to figure it out, I even put it on Desmos.

@lucys954 2 жыл бұрын

you saved me

@osssosos 4 жыл бұрын

what the "u" ??

@ProfessorDaveExplains 4 жыл бұрын

check out the tutorial earlier in the calculus playlist about u substitution

@miguelneo7767 5 жыл бұрын

Cedric alcantara

@trunkmonke 5 ай бұрын

you cant combine like terms when its more than one term, it will yield the incorrect results

@Eman-badr Жыл бұрын

thanksssssssssssssssssssssssssssssssssssssssssss

@tsegaynegash-dy4ev 14 күн бұрын

❤❤❤

@codexcodexcodex 2 жыл бұрын

👍👍😄

@grattitudetebogo9501 9 ай бұрын

If I could Like twice

@cirebondevelopment1381 2 жыл бұрын

Teu ngarti

@sirilandsariah 3 жыл бұрын

He is either Avi Kaplan or Jesus

@pabloolbap6478 2 жыл бұрын

Omg, Math Jesus

@jeanpierremattei4073 Жыл бұрын

Merci !

@mrutyunjayreddy2 4 ай бұрын

Baahubali....

@brandonhung9990 3 жыл бұрын

Your videos and examples are too easy

@yagnapatel3912 3 жыл бұрын

That’s how a tutorial works. You are taught easy example then practice hard.

@vanshparmar6337 Ай бұрын

Explaining this easily is illegal

@zenvewello Жыл бұрын

You can find the 4 essential things in DC, huge black community.

@aatrox5559 11 ай бұрын

i hate your intro so fucking much that im couraged to write things after which i would have been taken by the law enforcments but on the other hand you make helpful video so the credits over all are -1 and be better