+C, The Constant of Integration [What/Why]

For an indefinite integral, the constant of integration is usually represented with +C. It represents the constant that can not be determined while completing an indefinite integral without extra information.

If we have a solution to the function we get when we take the integral, we can find the appropriate value of C for the given problem.

0:00 Intro
0:15 Demonstration of where +C comes from
2:23 Process for finding C value

#+C
#ConstantOfIntegration
#Calculus
#Integral
#Antiderivative
#JoeCMath

[TheAmInventor]

Just added to my playlist of "the best calculus videos I have ever seen", beautiful explanation.

[manishhemantPiMan]

Thanks a lot! I have studied calculus from many teachers but mostly none of them bothered to explain the real reason about the plus c probably because it doesn’t matter much. Good to see teachers like you making separate videos on such small aspects too that make calculus beautiful

[mantai]

Everytine I miss out a C in integration, I lose a penny.

[etkpspz]

This is an Absolutely astounding video! I was straight to the point, and very clear. I never knew why there was a constant of integration because no one explained it too me well enough...but I now understand why there is a constant of integration! Thank you!

[dabu]

I followed along just fine! Good video! At some point in college I fell off and failed out of Calculus, but it was later on. I'm actually interested as to where I fell off, so I plan on continuing to watch your videos until I cant understand anymore. 😎

[thibaultl]

Wow this was super helpful and concise. Thank you for making this.

[theJesai]

thank you so much, this helped a lot :) i love the way you explain! how do you make sections of your 'presentation' highlight as you talk about those elements? :O

[realmehuhn]

"Constant of Integration", oof, so ominous. My new gamig tag for sure ❤

[dominicellis]

Differentiation subtracts one unit of information measured in degrees of freedom. Every time you differentiate you lose one possible term due to the lack of curvature of the constant function. Therefore, in order to gain that piece of information back by integrating we have to guess what that constant is by saying its something. This is why initial conditions are so vital, because there’s truly no way to know where you’ll end up if you don’t have an initial reference point. After all, you need at least 2 points to describe a line.

[NormalFerrari]

I got covid right before my final and missed this entire unit. now I’m watching this video 40 minutes before my final 🥲

[itsduo]

Sometimes you don’t add c and I don’t understand, what does it being bound mean?

[samanthahill]

I didn't know Dream did math videos