Finding the Area Between Two Curves by Integration

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.
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[@minusart5242]

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!

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The beauty of math youtubers

[@ramunasstulga8264]

An hour long lesson tells exactly the same thing

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

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That is math unfortunately.

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Yes it works after 2years!

[@user-hv6ef9ie1g]

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

[@CusPedro]

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.

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[@alejandroalmarza8447]

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

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

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How'd it go?

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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

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I appreciate you Professor Dave.

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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

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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]

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

[@drumpfbad5258]

@@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]

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

[@musawaleed224]

Excellent explanation thanks very much

[@waffle_chris2]

Thanks for the help!

[@xy6762]

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

[@Ok.9.]

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

[@MrMarkgyuro]

thanks professor!!

[@jakebrowning2373]

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]

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

[@Thaumius]

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.

[@citizenofreality2751]

Very well done!!

[@shinobu3532]

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

[@vaigarainila]

very nice video. Thank u, sir

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[@LaraSchilling]

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.

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

[@LaraSchilling]

@@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]

Great Lara!

[@jacobvarghese4722]

Bro made this easy to understand

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dude that square donut example is gold

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I love this stuff!

[@user-kd5sn9zx9h]

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Thank you sir❤😊😊😊

[@SurinderKumar-os5il]

Excellent sir

[@yazeedalshammari3838]

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

[@grattitudetebogo9501]

Beautiful man

[@HarpSeal]

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]

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

[@julianarens3908]

big help!

[@muhammadrafiq8203]

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.

[@yaasioncabdisamed335]

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

[@prismoandfriends]

wow, I really did understand

[@user-oj4tj8li4g]

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

[@arbaj03]

You can just draw it to understand right

[@JoylessBurrito]

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]

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

[@JoylessBurrito]

@@tommyswag69 thanks

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[@vikashgangatharan6118]

Excellent 👍

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Best ❤❤❤

[@jvg6877]

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

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[@user-kh8fj6ln3z]

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[@Versatile_Voyage]

Is this with the use of definite integral?

[@adanernestochavez1423]

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

[@ericyow6265]

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

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you saved me

[@egreeno]

What does the "dx" mean?

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geogabra ?

[@miguelneo7767]

Cedric alcantara

[@coolguy1873]

last two functions dont overlap?

[@ThOtherzz_]

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

[@ThOtherzz_]

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]

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

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[@halieberry9935]

I can confused where did you get x3/3?

[@carultch]

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.

[@trunkmonke]

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

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

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

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

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