Integrals: Crash Course Physics #3

Continuing with last week's calculus introduction, Shini leads us through how integrals can help us figure out things like distance when we have several other essential bits of information. Say, for instance, you wanted to know how far your window was off the ground. You can figure that out by using integrals, a tennis ball, and a stopwatch! It's all here in this episode of Crash Course Physics!

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Thanks to the following Patrons for their generous monthly contributions that help keep Crash Course free for everyone forever:

Mark, Eric Kitchen, Jessica Wode, Jeffrey Thompson, Steve Marshall, Moritz Schmidt, Robert Kunz, Tim Curwick, Jason A Saslow, SR Foxley, Elliot Beter, Jacob Ash, Christian, Jan Schmid, Jirat, Christy Huddleston, Daniel Baulig, Chris Peters, Anna-Ester Volozh, Ian Dundore, Caleb Weeks

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[crashcourse]

We made quiz questions to help you review the content in this episode! Find them on the free Crash Course App!

[joannalai]

felt my soul leave my body when she said "there's a reason it normally takes two semesters of university to cover the basics" bruh i'm here trying to teach myself physics within two days in university

[quitschi]

"If you watched our last episode, you now know everything about derivatives and how to use them."
That is a bold assumption, I must say.

[xoreign]

on calculus tests I used to add "+ C" to my name at the top, to remember to add it for any integration problems. haha

[ck]

being a physics teacher, i was very intrigued when i come across Paul Hewitt. He stresses a lot on learning physics conceptually for beginners, rather than mathematically. It changes the way i see my teaching and learning process for physics. Seeing some of the comments in this and the previous video, it reinforces that point strongly

[JamzGe]

Q: Why do they never serve beer at a math party?
A: Because you can't drink and derive...
:D (sorry I just had to) :D

[Pikachu]

For all those who are having a little difficulty understanding the maths, don't worry its half a semester of maths in 10 minutes. Make good use of the replay button.
Best wishes
A fellow Crash Courser

[Adraria]

According to wikapedia:
Velocity is the derivative of position,
Acceleration is the derivative of velocity,
Jerk is the derivative of acceleration,
Snap is the derivative of jerk,
Crackle is the derivative of snap
Pop is the derivative of crackle.
The scientists who named the last three must have liked their cereal...

[Nasuth]

The only problem with these videos is that the time limit doesn't really allow our teacher to go into WHY these things work the way they do, but they do still give a good general idea of HOW to do it, and that's still pretty good.

[treesbiologist]

I have an integral test tomorrow. I came here to procrastinate, but you got me.

[cuckoophendula]

I'm starting to wonder if there should be an entire crashcourse calculus before a crashcourse physics now...

[ASLUHLUHC]

Instead of the last two videos, CC should've redirected everyone to 3blue1brown's essence of calculus series

[Uejji]

I would be careful about saying that C is where the curve intersects the vertical axis. This is true for polynomials, but not for, for instance, e^x (where C+1 is the vertical axis intersection).

Great series so far. I'm really glad you're doing this.

[danielmercado]

I learned more with this video than with my 2 semesters at the university. We need a CrashCourse on Calculus! This was awesome; thanks!

[MrKostas]

I made the mistake of watching this at 1.5x speed to save some time.

[JuanGutierrez-nzkh]

I’m a chemist who has been teaching HS physics, and wanted to review some calculus and this video put so much together that will help me go back to explain the basics of position, velocity and acceleration.

[nontrivialdog]

i cant imagine how the avg viewer with no prior knowledge of calculus would actually understand calculus just by watching this video

[mustafaawadelkareem]

Waaaw, its amazing. I've spent 3 years to refresh my high school derivatives and integrals, and now in only 60 minutes I restored almost all Physics Stuff. Thank you very much

[e.hhampsen]

Never have i been more excited to find out how tall a window is

[leion]

God, I love the intro music to this series so much it's half the reason I'm watching it. I want a extended version that I can just listen to over and over again.