internet audience: "thank you so much, professor leonard!! you literally saved my grade in engineering math 😭" his students, specifically that _one dude_ : "yeah, i did your way, but i got no results"
The Integral 0:30 > The Area Formula restated 1:10 Definite Integrals 4:50 > geometrical interpretation 7:00 > Properties 16:00 >w/ Example 27:00 Note: Riemann Sums are the addition of n number of rectangles to approximate the area. Taking the limit of the sum adds an infinite number of rectangles, which gives the area. This is equivalent to taking the integral of the function. A greater n gives a closer approximation of the true area.
SERIOUSLY THANK YOU. I was SO LOST IN CLASS and FELT LIKE MAYBE MATH ISNT for Me or Im NOT SMART ENOUGH but you taught me so well. Time to ACE my EXAM. Also you teach very well(passionately) and enjoyed your class i wish more teachers taught with love. Definitely and Infinitely appreciate it.
Hey Prof Leonard, I just wanted to that your calc 2 video series will be the only reason I will pass this course. Your videos are still helping students succeed even 9 years after the videos were posted!
I procrastinate to say this but I m a jee aspirant, wants to become biotechnologist and my tution don't make calculas more interesting than him so I decided to walkout tutions in order to learn from him. You will be remembered sir for this!🙏
I love your videos, they help me do well in quizzes and exams. I will support your channel when I have the means to do so one day, keep doing what you do :;) Love from Pakistan
Area of triangle @ 10:50 is wrong, it should be (3*3)/2 and not (3*2)/2. Class is really not paying attention :P EDIT: ofc he fixes it seconds later...
So..., since the negative of an area implies the area under it (or a reflexion across the x axis) does that mean that the area implies a position on the graph, rather than being indicative of the total space inside an interval? (I'm not too knowledgable on what areas are either, so bear with me)
I think you can think of 'n' as the number of rectangles you would be making under a curve. So basically, you're making the number of rectangles go to infinity. Negative infinity wouldn't really make sense in that context, although I think someone else can provide a more rigorous answer to your question.
I think you're confusing angles with area. We're not concerned with angles here, we're concerned with finding the area. The equation sqrt (1-x^2) basically gives us a semi-circle and we want to find the area of half of the semi-circle (a quarter of a circle). Since we know the area of a circle is pi*radius^2, to get the area of a quarter of a circle, all we need to do is divide by four, hence, the answer is pi/4.
try watching some of his other videos for scope/backround, if you have already done that and still do not get it then review your notes. If you still do not understand try practice problems or review your precalc. By now you should understand, if not then all hope is lost
internet audience: "thank you so much, professor leonard!! you literally saved my grade in engineering math 😭"
his students, specifically that _one dude_ : "yeah, i did your way, but i got no results"
im so glad im not the only one who's noticing that *one dude* looool
He is on the right side of the class, by now you should know they are the dumb ones😂😂😂😂😂
The Integral 0:30
> The Area Formula restated 1:10
Definite Integrals 4:50
> geometrical interpretation 7:00
> Properties 16:00
>w/ Example 27:00
Note: Riemann Sums are the addition of n number of rectangles to approximate the area. Taking the limit of the sum adds an infinite number of rectangles, which gives the area. This is equivalent to taking the integral of the function. A greater n gives a closer approximation of the true area.
Thank you so much!
SERIOUSLY THANK YOU. I was SO LOST IN CLASS and FELT LIKE MAYBE MATH ISNT for Me or Im NOT SMART ENOUGH but you taught me so well. Time to ACE my EXAM. Also you teach very well(passionately) and enjoyed your class i wish more teachers taught with love. Definitely and Infinitely appreciate it.
I agree
you have been my calc 1 teacher so far
but you're my calc 1 teacher lilian
LOL TRU
yessir i’m self studying calc 1 for my next semester since i’m taking calc 2
he have been my precalculus teacher so far! -_-
@@jkgan4952😊
You are literally the best math instructor on
youtube. Everything was perfectly clear and easy to follow along!
I've skipped all my Calc classes since the first week thanks to your videos!! GOATED
Truly making university calculus simple. Ciao
Hey Prof Leonard, I just wanted to that your calc 2 video series will be the only reason I will pass this course. Your videos are still helping students succeed even 9 years after the videos were posted!
OSU need professors like you! thanks for teaching and sharing your lectures.
so does uo
whats osu
@@chill4r585 ohio state university
I procrastinate to say this but I m a jee aspirant, wants to become biotechnologist and my tution don't make calculas more interesting than him so I decided to walkout tutions in order to learn from him. You will be remembered sir for this!🙏
Thanks, mate. Really helpful.
You saved my semester!God bless you
YOU ROCK! Best lecture ever!!!
Thanks, for this video. Made my homework 40 times easier
Jesus christ, you are jacked as hell. Besides Calc man... How did you get so big?
THANK YOU I HOPE I GET STRAIGHT A'S IN MY UPCOMING QUIZZES AND FINAL CAUSE IM FAILING YOU'RE MY ONLY HOPE GOD BLESS U ILY
I love your videos, they help me do well in quizzes and exams. I will support your channel when I have the means to do so one day, keep doing what you do :;) Love from Pakistan
Thank you sir for your incredible effort... truly a mesmerizing teacher
whats your workout plan
Pushups!
Math problems
Erasing that board
@@zarinlubna5437 LMAOOOO
@@temiloluwaakande2358 😅
love you sir for lecture
You explain very well but in properties 4 you can use bracket it is very important.
Area of triangle @ 10:50 is wrong, it should be (3*3)/2 and not (3*2)/2. Class is really not paying attention :P
EDIT: ofc he fixes it seconds later...
Thanks, prof. Life saver.
Best math professor
you are ,,The Teacher ! '' professor.
Thank you sir thanks🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🌹🙏🌹🌹
YOU ARE THE MAN
math daddy af
thanks man
Thanks for your videos, Prof Leonard.
Thanks you very much, this was so helpful.
Finally, i heard he said "Riemann sum"...in this video....
King 👌🏼
SO GOOD
Great video thanks
man u r so cool
Waittt noooo I need more vids like this
damn - I laughed at 20:02. i'm reviewing rn and did a tedious trig sub - I forgot you could make it that easy.
Outstanding
So..., since the negative of an area implies the area under it (or a reflexion across the x axis) does that mean that the area implies a position on the graph, rather than being indicative of the total space inside an interval? (I'm not too knowledgable on what areas are either, so bear with me)
thanks for this video
Thank you!
I love you Professor Leonard. btw, you are a hottie.
I couldn't understand the second property of definite integrals at 20:40 ... Can someone please explain
"alot of effort, not a lot of results"
You can practice here! algebry.com/algebry/calculator/Calculus-I/Definite-integrals-calculator/
please tell me that if integral evaluates area then why can definite integral be both positive and negative and area be always positive only?
It si because f(Ck) becomes less than zero for some values and hence area with the sigma notation becomes negative
By the 6th property, wouldn’t the integral of any odd function be equal to 0 given the interval [-x,x]?
0:50 "is this still 4.3"
u save me grsde thx. alswo, nice cwock bro.
thank you boss
in which university is he giving lectures?
does every summation that goes to infinity become a integral?
sorry for the grammar, i'm italian
so buffed lol
thnk u sir merci for the vid .sir stp can u give as some pdf "homework site" as yournet students plsssss merci
@ 7:05 does it have to be the lim as n approaches positive infinity or can it be negative infinity?
I think you can think of 'n' as the number of rectangles you would be making under a curve. So basically, you're making the number of rectangles go to infinity. Negative infinity wouldn't really make sense in that context, although I think someone else can provide a more rigorous answer to your question.
professor leonard my friends think you're handsome
11:03 area of trapezoid doesnt give us 6, it gives 7.5
oh ok
can someone explain how did we get height 3 at 11:49 for the triangle
+Rim Oo Because if you look closely on the board the triangle begins at y=1 and ends at y=4 so you subtract 4-1 to get 3.
Some prof never explain the concept.
9:53 Trapezia: You've forgotten our definition.
24:30
the guy who is making jokes and said something like "fingers crossed" has an amazing voice. well , find me
he's cute
عربي
Praise Jesus
Pi over 2 not 4 because pi is180 and 1/4 circle is pi over 2.
I think you're confusing angles with area. We're not concerned with angles here, we're concerned with finding the area. The equation sqrt (1-x^2) basically gives us a semi-circle and we want to find the area of half of the semi-circle (a quarter of a circle). Since we know the area of a circle is pi*radius^2, to get the area of a quarter of a circle, all we need to do is divide by four, hence, the answer is pi/4.
bhag
still dont understand *AT ALL*
try watching some of his other videos for scope/backround, if you have already done that and still do not get it then review your notes. If you still do not understand try practice problems or review your precalc. By now you should understand, if not then all hope is lost
It helps to solve some problems by yourself after learning the concepts. Khanacademy has A LOT of problems you can solve.