Applications of Integration - Free Formula Sheet: bit.ly/3ZdKSnK Final Exams and Video Playlists: www.video-tutor.net/ Calculus 1 Final Exam Review: ua-cam.com/video/WmBzmHru78w/v-deo.html Next Video: ua-cam.com/video/df1Qr8pepx0/v-deo.html
The difference between part 1 and part 2 for those who don't know is that for part 1 we found the derivative of the antiderivative F(x) but here we do not do that step and just plug in the values to F(x) and solve for it
Professor Organic Chemistry Tutor, thank you for a basic introduction to The Fundamental Theorem of Calculus Part 2. This is also another important theorem in Calculus. Professor Organic Chemistry Tutor, although the final solution is correct in all your examples, equal signs are missing in between the problem and the final solution. Please correct these small errors in the video.
you're right. it is because some textbooks explain how to evaluate the limit definition of a integral before showing the fundamental theorem of calculus. therefore using that definition, they are able to take the definite integral. Then in part 2, they learn how to apply the Leibniz notation for the definite integral. That is my best guess as to why some textbooks show it in the same order Julio did in his videos.
Why never add the constant (“C” ) when you resolve the anti derivative F(x)? For the first exercise (1:32”), (3/2)x^2-4x +C, shall we at least keep the “C”here to make the equation true?
Because its a definite integral which describes the area between a and b. If you used trapezoidal method or riemann sums you will see they approach the definite integral.
because when you use the fundamental theorem, you do F(a)-F(b). imagine F(x)=x+c so if you did the fundamental theorem, it would be (a+c) - (b+c), which would automatically cancel the c out, giving you a+c-b-c = a-b. i've found that a lot of teachers just omit the c entirely in FTC problems because it cancels out anyway.
First part allows us to find the derivative of F(x) while the second part allows us to evaluate definite integrals by evaluating F(x) from a to x. Stated otherwise, the first one gives you the instantaneous rate of change of F(x) while the second one gives you the area under the curve of the function f(x) in the interval [a b].
why would you divide 18 by 2? Since F(b) = (75/2)-20 and F(a) = -2, shoudlent the result of F(b)-F(a) be (75/2)-20+2? From my understanding (75-18)/2 would be the equivalent to (75/2)-(20/2)+1 Genuine question I'm tryna learn calculus rn
A much easier method of solving the integral of (2x - 3)^2 from 1 to 4 is using u-substitution. Just let u = 2x - 3 and change the limits to -1 and 5. Don't need to FOIL the binomial and integrate each part. You'll get 126/6 = 21. Done.
@@GillAgainsIsland12 I SEEE. so u plug in the old values into whatever U is? and make those the new limits. do u do this for every definite integral u solve with U sub?
Applications of Integration - Free Formula Sheet: bit.ly/3ZdKSnK
Final Exams and Video Playlists: www.video-tutor.net/
Calculus 1 Final Exam Review: ua-cam.com/video/WmBzmHru78w/v-deo.html
Next Video: ua-cam.com/video/df1Qr8pepx0/v-deo.html
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The difference between part 1 and part 2 for those who don't know is that for part 1 we found the derivative of the antiderivative F(x) but here we do not do that step and just plug in the values to F(x) and solve for it
Finally, a short enough description to put on my flashcards for FTOC pt 1 and pt 2 lol
Thankyou John ortiz
🐐
Of coz
No as for me I think the difference is in case 1 the interval has a x limit while the case two the interval has only integers
His "In this video" is the best and foremost anti anxiety med I have ever taken.
I literally couldn’t have passed any of my 1st year of cs exams without you
This guy is the living proof of Math is not difficult; it just requires a good tutor.
I always watch these videos, even if I am very confident in my understanding of a subject because he always shows me something I didnt know before.
why does this make so much more sense than what my professor has been doing?!?!
explaining/teaching is an art.
My Calculus II professor has this thick Russian accent, so it was really hard for me to understand when English is my second language.
@@kennyhuang7393 i feel that, my teacher as well in BC Calculus has a very thick Russian accent and broken English.
@@kennyhuang7393"no more than one unmarketable tomato"
@@nexon7610 BAHBAHDBJHAFBGJHASF no one understood i guess
OCT: "In this video, we are gonna talk about..."
Me: Immediately understands the concept
Him: "In this video..."
Me: "YES God! Is that you God?"
What would we do without this guy?
Hlw
whotrekkie R I don’t know about everyone else but for me F A I L
spend time reading the confusing af stuff in the textbook
an absolute legend
So it's basically definite intergrals, right?
Iol i know right
Haha lol same
I was looking for this comment
@@marajoyf i was looking for this comment too
I was looking for this comment
i thought the part 2 was just my teacher dividing it up
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Thank you so much for this clear and easy explanation, God bless you
universities should just show this guys videos. makes way more sense than some old ass dude trying to use words he doesn't know
Love your videos...I have been learning from them for over a year they are great and explain the concepts very well. Thank you
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Great explanation keep uploading this kind of videos BRO
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Great videos! keep up the good stuff
I use JG as a verb. “Son, I don’t remember that stuff. Give me a second and I’ll JG that stuff.”
Professor Organic Chemistry Tutor, thank you for a basic introduction to The Fundamental Theorem of Calculus Part 2. This is also another important theorem in Calculus. Professor Organic Chemistry Tutor, although the final solution is correct in all your examples, equal signs are missing in between the problem and the final solution. Please correct these small errors in the video.
I love you so much man
Why is this part 2 when the techniques used in this video were required for part 1?
That is why in some textbooks it is the first part of FTOC
you're right. it is because some textbooks explain how to evaluate the limit definition of a integral before showing the fundamental theorem of calculus. therefore using that definition, they are able to take the definite integral. Then in part 2, they learn how to apply the Leibniz notation for the definite integral. That is my best guess as to why some textbooks show it in the same order Julio did in his videos.
Why never add the constant (“C” ) when you resolve the anti derivative F(x)? For the first exercise (1:32”), (3/2)x^2-4x +C, shall we at least keep the “C”here to make the equation true?
Because its a definite integral which describes the area between a and b. If you used trapezoidal method or riemann sums you will see they approach the definite integral.
because when you use the fundamental theorem, you do F(a)-F(b). imagine F(x)=x+c so if you did the fundamental theorem, it would be (a+c) - (b+c), which would automatically cancel the c out, giving you a+c-b-c = a-b. i've found that a lot of teachers just omit the c entirely in FTC problems because it cancels out anyway.
@@sofiawong9681 great explanation!
Because later you take the derivative of the expression so the constant cancels out
Thank you 💛💛💛
Well explained
This videos will forever help me pass
All heroes have a catchphrase... this one is: "In this video"
You videos have helped me😉
Whatever you get paid, it isn't nearly enough of what you deserve
Thank you 🙏
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Thanks mate!
Hello..please have you covered Leibniz's theorem in any video
Thanks!
Thank you!!
You never know you are going to do for the next step in calculus
Nice, thank you
plozed inerval / inerfal
at 10:03 why is 1 ^3/2 1?
Anything raised to 1 is just 1
Ur my hero
SAVED MY BEHIND!!!
May God bless you
I always feel I am passing whenever I watch these videos,
Whats power rule? The normal one in derivatives?
ahhh thank you!!
POV: watching this 40 minutes before your proctored exam
so the second part of the theorem is essentially finding the area under a curve
yes I will pass now
so its just definite integrals
So there is no difference between the FTC Part 2 and doing definite integrals. Interesting.
What apps are you using for writing all this math equation?
Probbs microsoft paint.
Why the first and second part is different? And how we know which one we will use for the question.
First part allows us to find the derivative of F(x) while the second part allows us to evaluate definite integrals by evaluating F(x) from a to x. Stated otherwise, the first one gives you the instantaneous rate of change of F(x) while the second one gives you the area under the curve of the function f(x) in the interval [a b].
do you know how to find the anti derivative, im kind of confused @@No_BS_policy
Bro I start Calc 2 tmr and i got scared asf and started doing some last minute studying bc i forgot everything
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why F(4) - F(1), not F(4) - f(1)???????
You need to subtract integrations no the main equation
My midterm is tommorow :(
same
The answer for the first is 57/2 and not 39/2 (3:00). As it becomes 75-18/2, and 75-18 is 57.
why would you divide 18 by 2? Since F(b) = (75/2)-20 and F(a) = -2, shoudlent the result of F(b)-F(a) be (75/2)-20+2?
From my understanding (75-18)/2 would be the equivalent to (75/2)-(20/2)+1
Genuine question I'm tryna learn calculus rn
I love you
A much easier method of solving the integral of (2x - 3)^2 from 1 to 4 is using u-substitution. Just let u = 2x - 3 and change the limits to -1 and 5. Don't need to FOIL the binomial and integrate each part. You'll get 126/6 = 21. Done.
why change the limits
@@adesolao.2585 Because the old limits were x values, the new limits are u value where u=2x-3.
@@GillAgainsIsland12 I SEEE. so u plug in the old values into whatever U is? and make those the new limits. do u do this for every definite integral u solve with U sub?
@@adesolao.2585 I do 😉
Can you please be the professor at my school
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So thats why we do some weird stuff to get the limit to be from zero. So the equation gets canceled.
meow
Easy much?
First to comment
Marry me please. College gpa saved
This is wrong
how?
Idk about you but I aced my exam after learning this from the video and his other one
Wrong not to learn from?
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