What is Integration? Finding the Area Under a Curve

Ok, we've wrapped up differential calculus, so it's time to tackle integral calculus! It's definitely the trickier of the two, but don't worry, it's nothing you can't handle! First things first, what is integration? Well it's that thing we mentioned way back in the introduction clip, when we talked about adding up the infinite tiny rectangles. Just watch and you'll see!

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[tbax]

Dear Professor Dave, you explained integration to me in just under nine minutes. WOW. Thanks, Professor Dave. I am now your happiest patron!

[Gee]

As a programmer who didn't learn calculus, integrations or anything else like that, this is GOLD. Thank you!

[varunn.a.]

My teacher never taught me all that when I was at school...When I watched a video related to entropy, I got scared by the integral sign just like the way I got when I was back in high school. I work as an automation engineer in food and pharma sector and have watched some of your nice videos related to pharma industry. Now I have got the clearer idea of why integration is important and hoping to make use of the knowledge in future. Now I also realize how bad the situation was for us before these videos become available. Professor Dave inspires me to face my old high school and college demons and win the fights I lost back then. Teachers like you provide us with an opportunity to fix the gaps we had in our early education and provide us confidence to upgrade our brains for the future....Great Video and wishing the best for you and your channel😃

[sarahfox]

You are literally my Calc II teacher right now thanks to distance learning lol so THANK YOU!! This was very helpful!! We need content like this now more than ever.

[therealdeal]

Nice, this is way better than binge watching Netflix.

[drewpetersen]

Your videos are explained so well! Thank you! The time put into these animations really reflects the viewers ability to understand it as well! Keep it up!


Also this unit is actually pretty interesting. I never thought I would hear myself say math is interesting but seeing how calculus finally folds out is kinda cool.

[ripperduck]

I very much appreciate the work you've put into your series of vids. But, the problem is that no one explains why calculus was invented, why it works with physics, what the area of an integral is suppose to physically mean, on and on. As a guy with a BS Physics, not one professor, nor textbook, ever bothered to explain/lecture the 'why' of math, which meant, that for many years, we were doing things by simple memorization.

What I learned is that the most important math concept is that of the pure number. Derivatives and integrals are pure numbers, as are fractions, ratios, percentages, geometry, trig, slopes, thermo entropy, and a bunch of other things. In other words, we were introduced to the overarching concept of all calculus back in the third grade, but no one bothered to explain its importance. I wish STEM vids would begin teaching the fundamental concepts of their disciplines prior to doing problems, that way the subject matter would be far more engaging...

[joeykenn]

An excellent simple well illustrated explanation. Thank you very much.

[deeguy]

Thank you for explaining how to identify the part of the equation that identifies the height of the rectangle and the part that identifies the base. I will not move on to fourier transforms until calculus makes sense to me. I think I need to work on a few examples to let it sink in.

[apostolosfilippos]

I hated this for over 20 years. Explained in 8 minutes. Thank you!

[Kiky_MedPhysicist]

Thank you sir for your dedication and for making this free! 🙏

[isaiahrichards]

Wow, this really helped me to understand. Thank you very much!

[niv]

Ad: still search for math help are the videos from 2006 really helping?
Me :yes

[odileabimana]

you saved me. Thank you so much for this tutorial

[Maryam-dqiy]

Thank you very much for your effort in explaining these hard topics, really appreciated

[scoopboy]

Proffessor Dave you game an epiphany at 3:33

[AA-eqwk]

the quantum wave function is a positive AND negative swing which "differentiates" the parts or two poles that make up a whole; the "integration" is then taking that entirety and making a "relativity" or relative observation which is not true to the whole but polarized... in order for a 3 dimensional life form to interact with a solid or 3-D world, the observation must polarize the wave function so that it can be compared to other measurements or become a finite piece in an infinite whole...

[siddhantshenvi]

Superb explanation...it's crystal clear...Thank you so much Professor Dave!!

[Thaumius]

Hey Dave, my teacher taught us about left hand rule, right hand rule and midpoint rule, how do you implement them into the summation formula (Riemann sum)?

[minorfirestar]

Thank you so much for the Calculus videos, Professor Dave! I'm about to take a CLEP exam for Calc. and the study videos I originally used (by Modern States) were no help at all. More people need to know about you!