Finding the Area Between Two Curves by Integration
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- Опубликовано: 26 авг 2024
- 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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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!
The beauty of math youtubers
An hour long lesson tells exactly the same thing
@@ramunasstulga8264 the explanation on lections is sort of more complex i think..
That is math unfortunately.
Yes it works after 2years!
man u explain 1 1 hour lecture with animations in 10 minutes - this is amazing!!! thank u!
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True dat
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OH MY.. AN HOUR LESSON OF THIS AT MY UNI DIDN'T MADE ME UNDERSTAND A SINGLE BIT. BUT A 7 MINUTE VIDEO ON RUclips DOES. THANKS DAVE!
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.
Thank you, professor Dave. Your way of explaining is sooooo sweet. Please keep it up. You've helped me today
Finally, youtube algorithm does help. This is gonna be a huge help in my oct/nov 2020 as exam.
How'd it go?
Excellent explanation….clear as water and better than any of my College PhD professors…keep the great work.
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!
Dont you still have to take Pre calc and Calc AB?
@@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.
In 7 minutes you explained this better than my professor did in 2 hours! Thank you:)
such a shame i had my add math exam 2 days ago
this would have helped
Malaysian bro?
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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.
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?
If you calculated an interval that goes past the intersections you did something wrong...
great video! explained clearly and precisely!
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
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.
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.
idk you but that sounds freaking awesome and i'm so proud of you!!!
@@uggo2488 Thank you! I haven't done any calc in 2 years, so I've forgotten everything xD
In one ear, out the other.
Great Lara!
Dude, that analogy at the beginning made it all click together, ty sm
Thank you bro, I have my calc exam tomorrow, this will greatly help.
You make it seem so easy. Thank you sir🎉
That was very helping I was confused about this matter for a time that was easy to understand in a quite short time thanks
Thanks for the help!
This gives me more knowledge than my two hour lectures. Thank you so much
What if the intervals are not given? How can you determine the intervals of each function and find its area?
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)
You can find the boundaries by setting the functions equal to each other to find where they intersect.
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?
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
Excellent explanation thanks very much
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
yep the problem is me, ive seen around 20 vids and couldnt understand a single one.
Your explanation is just amazing
Thank you
Is this with the use of definite integral?
yes, at the end you should get a number and not +c
I appreciate you Professor Dave.
In 7 minutes you explained better than my teacher's 2 hours lecture 🫡 Thanks man
Thanks man i got a test tomorrow this will definitely help me
Pro, give me advice because I never understood Physics and Math. What I do
What does the "dx" mean?
Hello professor Dave, please how do you know which of the functions is the upper function and which is the lower function.
You can just draw it to understand right
dude that square donut example is gold
thanks professor!!
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Bro made this easy to understand
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?
I'm probably way too late but it'll even itself out, the logic works the same way
@@tommyswag69 thanks
very nice video. Thank u, sir
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Excellent sir
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can someone help pls.. what does it mean when i integrate a function with (a,b for eg) i get 0
wow, I really did understand
Very well done!!
I love this stuff!
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
Thank you sir❤😊😊😊
I can confused where did you get x3/3?
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.
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check out the tutorial earlier in the calculus playlist about u substitution
last two functions dont overlap?
yes bro ive been trying to figure it out, I even put it on Desmos.
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you cant combine like terms when its more than one term, it will yield the incorrect results
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Your videos and examples are too easy
That’s how a tutorial works. You are taught easy example then practice hard.
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