Integration

Integration is one of the beautiful pillars of calculus. It revolves around the idea of doing the opposite of differentiation, an anti-differentiation. Sounds straight forward right? However, there is an unbelievable connection which revolutionized mathematics entirely! That result is that anti-differentiation is equivalent to the area under a curve. In this video we take a deep dive into integration and explain why it is the area under the curve.
Problem Sheet: mathacy.com/problem-sheets
Timestamps:
0:00 - Intro
1:15 - Inverse Operators
1:45 - Integrating x^n
2:46 - Adding a constant
3:44 - Integrating cos(x)
3:53 - Integrating exponentials
4:10 - Integrating 1/x
5:18 - Area under a curve
6:14 - The link between Area and Integration

[@lyricass7810]

The way you gave an introduction to integrations, I have to say, it gave me goosebumps. LOL :)

[@aaronnanoo1887]

The best video yet, with outstanding animations. Trapezium rule animation was really useful to better grasp the concept.

[@maruffayzullayev9684]

❤

[@aleenavirdee5656]

Amazing video, explained so much better than it was in school. RUclips needs to up their game and recommend your videos first - A level Maths students everywhere are missing out!

[@DiLLZGFX]

You've done it again ! Amazing stuff !

[@gurpritkaur3795]

This was so engaging! Love how easy it is to follow.

[@Dinesh123lol]

One of the best explanations I have ever seen, thank you! 👌

[@TheHashCam]

Awesome!! Love the animations they illustrate the points so well!

[@amybajwa15]

Your videos just keep getting better and better 👏🏽👏🏽

[@navneetkaur2445]

Brilliant video and very easy to understand

[@skaur6838]

Once again another amazing video.. very well animated and clearly explained 😃👏👏👏xx love it 👏

[@pressingericrizo]

My mind is being blown this is awesome

[@mirajsounds]

So clear!

[@jsingh6931]

Great video and explanation well done 👏 👌

[@sukhibhamra5750]

Amazing well done 👍🏻👏🏻👏🏻👏🏻

[@geamer0079]

Very high quality this channel deserves more views and likes

[@micheledellavalle603]

YOU'RE FANTASTIC!

[@kitnex5486]

You‘re doing such a great work! I can‘t believe you just have 7k followers

[@harbanskaur460]

Well done

[@iamtrevor1551]

ur content is outstanding but i suggest u should also keep an eye on promoting
there are really very few channels like yours

[@shashanks8017]

I request you to upload videos on limits and continunity r by the way your videos are awesome❤

[@user-zs9cl2to3x]

Amazing stuff. However Integration problem sheet link leads to Integration by parts problem sheet. Is it expected?

[@philippelhaus]

Gold

[@bobmichael8735]

what software do you use to make your great videos?

[@gustavomarcelo6938]

There seem to be a problem with the exercise sheet, because it isn't the normal integration one, it is the integration by parts sheet

[@abcdef2069]

what took me into a nightmare thinking about the logical steps of an integral was that dx in integral [f(x) dx, from a to b] was ALWAYS positive. i had no problem understanding in riemann sum, sigma [ f(x sub k) delta x, k from 1 to n, n goes to infinity ]. but example, integrate from b to a (b>a) i thought this makes dx is negative. about the interval from b to a in which the direction also makes negative, and the area should be positive for both cases, why would it matter if you do it from left OR right. maybe hope to see your explanation in this pitfall.

[@user-ky5dy5hl4d]

When you integrate then you add a constant. Why can't you subtract a constant?

[@EMECATRONICOS]

code please

[@pberPSR]

Haitch != aitch

[@jameeztherandomguy5418]

???

[@skrrskrrrr99]

here before 1 million views ezz