Average Value of a Function on an Interval Using Calculus

[@Newbport849]

[Insert generic "You've helped me so much in understanding this topic compared to my professor" comment here]

[@thomassteil7099]

really helped out, thanks so much, aced my test thanks to this. Really glad people like you do what you do. Cant thank you enough.

[@ilovemusic24ful]

That would be so incredibly awesome. So, I decided I will be donating money to you monthly. Your teaching style has made a huge difference for me. Thank you so much for your amazing videos.

[@justinortega9474]

imagine just flying through this like patrick did

[@reykjavik07]

I really like your videos. Thank you so much! I am an engineer and I don't use this math so often, so it is good to remember those things now and then.

[@ShadowDweller]

Jesus you are a life saver. I have a calc teacher that I can barely understand Bc of his accent and I had a quiz to take today and I watched these and it helped a lot thanks :)

[@val3306]

These videos have literally saved my life so many times. Thank you:)

[@EvaMarieCalzado]

You saved me in Ap Ab calc today !!!!!! Thankyou

[@Californiway]

This is why I love math!! It gives you so many formulas where you can solve any basic problems

[@kwanele1253]

I did not attend this on the lecture. I never thought it was this simple. thanks a lot, this was every clear. :D

[@annastasia8733]

I have a quiz in 2 hours thank you.

[@Flareblade26]

life saver! Thank you so much I couldn't even find this in my calculus book!

[@naulyd]

thanks to this, i blew through my average value of a func questions as much as you blew all over your microphone

[@FlameXGaming]

when your teacher is telling you what youtubers to watch for calculus and she says "NEVER WATCH PATRICK" cause he explains little, and then l am like, he cares less about the unnecessary stuff and explains what we actually need to know clearly and efficiently, cause no one has time for the dumb stuff, patrick you are awesome

[@patrickjmt]

thanks! never watch patrick (the most popular math channel on youtube!). the point is: your teacher is supposed to be explaining things. i am here to supplement. maybe your teacher does not understand that. feel free to explain it if need be :)

[@ThePharphis]

Area, (the integral) divided by average length (b-a) = average height, since it is variable. I think is a pretty clear way of explaining it, as I just came up with this on the spot to justify it to myself, and I think it makes sense. This will probably help with my Quantum Chem final. . . Thanks!

[@vivekbharti12]

I am so much envious of your handwriting.

[@anthonymmeek]

you could literally redo all your videos just to update them, and remake money cuz I know I'd watch them haha. Love your channel, bro

[@sahilms]

got an exam in 2 hours I just found out this was on there :| you saved me sir

[@yamdeu]

i just blew through hours of calc homework thanks to you!

[@somaia2793]

Greetings from Egypt :) Thanks for all your videos :)

[@ahmedelnageh507]

Patrick, you're a legend

[@patrickjmt]

ha, you are too kind!

[@patrickjmt]

you are very welcome!

[@ljtan4676]

U da real mvp, sir! thanks!

[@humiraarroyo]

you're so easy to understand!! thanks for the clarification!!!

[@patrickjmt]

happy to help :)

[@JaviGomez]

How can you find where the function assumes its average? I'm guessing you set the function equal to its average?

[@outsidegirl100]

You rock Patrick!!

[@SeaPen]

When do you know when to use average value?

[@XxKingBolandxX]

how do you know when you should use the average value theorem?

[@timmychung5673]

thank you so much this was a great help!!

[@xturbospyderx]

That is odd... the James Stewart text (7th ed.) that we are using currently actually labels this "The Mean Value Theorem for Integrals" about halfway down page 452 ... why would you say this in not the mean value theorem?

[@supernintenjoes]

Thank you so much! You're the best.

[@shaiknoor6381]

wow i understand it very well.Thanks a lot.

[@sh4673r]

Thank you, that was very helpful

[@codymacification]

what about when you are computing the average value of a double integral. I know it is "1/area of the region", but it my area found by integrating once then putting that in...or are my bounds for both x and y what i use for the denominator on the Fave. I am way over thinking this I think.

[@xulu7906]

that is a really good video! thanks a lot!!

[@DoggoWillink]

No, this isn't the Mean Value Theorem. I'd review it, if you have the time. It can't hurt. It's always good to remember the stuff from Calculus 1, since it's pretty fundamental. It comes back to haunt you out of nowhere.

[@benjaminjmiller]

Quit going to calculus two months ago. I'm going to get a B. Thanks!

[@Medic1911]

can you do a video on how you solve complicated problems with trig involved or stuff to negative powers? I know for those you use u and du but I dont understand how.

[@SuperSpable]

that's called U substitution which he has a video on!

[@Medic1911]

thanks so much man! rock on~

[@fcinternetmarketing]

Thank you for sharing.

[@m3gadinum8]

in my text book.. it says that this is integral mean value theorem.. so its the same right?

[@algator1730]

Is the mean value and the average value the same?

[@MohamedSharif7]

Is this the same as the mean value theorem?

[@chadmessier6285]

Once you have plug 3 and 1 in for x.... How do you know to subtract them?

[@fuzzygreen3634]

thats how you calculate definite integrals, he just didnt explain it in detail because at this point you should know that

[@josephmarch7501]

what about with trig functions??

[@CoolStoryBro26]

youre amazing! thanks a lot :)

[@g.taurus5162]

thank you so much

[@B.A.Gondal]

What kind of math do you use then?

[@ThePharphis]

I meant to say length, not average length. So it's area/length= average height

[@rashwonsingkai7955]

How to do it for an area??

[@7L00]

thank you

[@nosheentaj472]

send me the solutions of the problem of a average value of a fuction. problem section 4 of Mary lboas

[@averageguysgadgetguy]

Im confused...isnt 3^3 =9 then 9/3 = 3?

[@micahhhhhful]

I'm sitting here thinking the same thing. Hoping somebody else would notice this same mistake and I wasn't going crazy.

[@BlakaveliX]

3^3 is 27

[@micahhhhhful]

oh yeah hahaha

[@cnscm2614]

+Micah Decuire you're pretty

[@BlakaveliX]

*Throws a bottle of Aquafina at **cnscm2614*

[@ladiipil]

Homework help please The temperature on a July day stars at 60 degree at 8am, and rises to 96 degree by 8pm. Assume the temperature is a non decreasing function of time. A. Why can't you say with certainty that the average temperature between 8am and 8pm was 78 degree? B. what can you say about the average temperature during this twelve hour period? C. Suppose you also know that the average temperature during this period was 84 degree. Is it possible that the temperature was 80 degree at 6pm? At 4pm?

[@AmatuerAstronomer2014]

Still need help?

[@Syruscleat]

Wonderful!

[@palizle]

i wish i could give my tuition money to you

[@jyaswanth9688]

Can the average of the function be zero???

[@altuber99_athlete]

Yes. The average of a simple sin(x) or cos(x) is 0 for any complete cycles.

[@smitrib]

yay thanks!

[@FlashGamer1Fable]

WHAT THE FUCK How did I teacher manage to screw this up?!

[@holygod199x]

Why didn't you give us an explaination of average value? You just provided the formula and showed how to use it...that's it? Oh men, where can I find to video explain how the formula work?

[@patrickjmt]

no

[@beverly6240]

Thanks!!!! :)

[@hemanthtaliya4188]

thanks :)

[@mrmathman202]

I get it now

[@rasoolzada2334]

Great!

[@nomealow]

the first second in this video sounded like a girl

[@nosheentaj472]

please send me now

[@maryamal-mohanadi3834]

t h a n k y o u

[@Milkacow77]

Buy a different larynx. Your voice "derives" me crazy

[@SmiteThyFace]

what do we do if its a piece wise function?