[M4F] Don't Forget the C

Transcript

Alright, welcome back. Sorry, I'm just stretching. It's been a long day.

I've had how many? Three? No, yeah, three.

Three sessions before you. End of the day. Don't worry about me.

I'm just being a little bitch. Oh, I'm sorry about the language. You know, we don't care about that here.

Well, anyway, why don't you just take a seat and get your textbook out and show me. Actually, I do remember I've got some notes here. There we go.

Ah, you were, we were finishing derivatives last time. So your curriculum is about to enter the next step after derivatives. And hopefully by now you understand kinda what derivatives are.

It's an analytical tool, essentially. You analyze functions and also curves and other things. You simply just check the slope of something.

If you really want to be simple about it and visualize it, that's what it is. You're just checking how much something is changing. Either that's, you know, upwards or downwards or in 3D space as well.

You can have a derivative off of a curve if you want. Yeah, it doesn't matter. It doesn't have to be a function.

It's very useful in many cases to just check when something turns, how much it's turning. You can kind of sort of extrapolate things based on current trends. All sorts of useful cases.

However, you can also go the other way around. And this can be, this is a bit of a problem when you remember that if you're taking the derivative of a function, let's say x squared plus three minus two. Well, you take the power and you multiply it in front, then you reduce the power by one.

So x squared, you take that two, you multiply it in front and then you reduce the two by one. So that becomes just x, well, to the one power. So it's just x.

So that makes it 2x. Then I said plus 3x. Well, the x is already a power of one.

You reduce that. Well, you can technically, you can multiply that one in front. It's not going to change that three.

It stays the same because obviously you're just multiplying by one. You reduce the one, the power by one again. So that makes it 3x to the zero of power.

And what's anything to the zero of power? It's one. So you essentially get one multiplied by three multiplied by one.

So you're just, you're just left with a number. And that's all fine. It's easy to remember.

You can just cut off a single x if it doesn't have a power symbol on it. And then the last one, minus two, you just delete it. Easy, simple as that.

It's not relevant to what you're doing. You're actually taking the derivative of a variable, of a specific variable. We don't mention it all that often, unless you do the whole Leibniz notation, like dx dy.

But we don't really care about that right now. We just want to get the basics in and you just want to pass the course with a decent grade. You've got a lot to learn.

So let's just get started with integrals. Let me think of something. 4x plus 3.

What would be the integral of that? Now, remember you have to do the opposite way around. So let's start with the things that we do know.

We know that that x is going to increase its power. So it's going from x to the 1th power to x squared, right? And that means when somebody in the past took that derivative to make it into that 4x plus 3, it was x to the power of 2.

But that means also they had to multiply that 2 in front. What multiplies by 2 to make 4? Well, that's 2, right? So you have 2x squared.

If you take that derivative, you go back to 4x. So the first term is 2x squared. Then that 3, well, you know what happens when you have anything that's just a number.

Or rather, you know what have happened to it. You just slashed off that x. So we can just put it back.

So we get 2x squared plus 3x. But then we have a problem. We don't know, there's no trace of what constant term there would be in this function, in the original one.

We don't know if there was a plus 7 or minus 2 in that original function that you took the derivative of to arrive at what we have here. It's just deleted information. It does not exist.

Unless you read some part of the problem or you've got some intuition that makes sense, or you're just an expert in whatever you're actually working with. If this is applied to a real life situation, chances are you might actually have a number. But generally, you don't.

You don't know where that constant was. So we just write plus C. Remember the plus C.

Don't forget it. I will subtract points for that. Well, that's a crash course introduction to integrals, the opposite of derivatives.

How about you try some yourself? And I realize I didn't really properly look over back at you to check if you're paying attention. How's it going? Does this make any sense to you? Or have I just been rambling? You know, I do that sometimes.

Well, hopefully your teacher taught you at least some parts of this, right? You couldn't pay attention. That's why it's good to have me.

Well, okay. Yeah, well, I would agree if it weren't for the fact that you're not really paying attention here either, are you? No.

I can see that this went straight through your head. Listen, I know it's been a long day. It's probably been a long day for you as well.

Did anything happen? Are you okay? Are you able to to do this? We've still got like how much on basically two hours left.

We're going to do some maths here. And I just want to make sure that you're in shape to do that. If you need to call in sick, you know what to do, right? You just call me before or send me a text.

I just need to know, right? I'm not your teacher. I'm not here to scold you.

I'm not your dad. I'm just I just want you to do well in this course and not fall off. You know, like you've done before.

Yeah, well, I'm here to I'm here to hold your hand through this and help you. So tell me what's up. Why can't you concentrate today? You're distracted.

Yeah, well, I can see that. Distracted by what? Is it something back at uni or family or friends or boyfriend or girlfriend or them friend or any, any social issues causing this?

Because I mean, I'm here to teach you maths, but. Well, I have to get results done, too. So if part of it is to listen to your woes, then I'll do that as long as you promise me you'll do you'll put in some proper work with me.

Well, I'm not your psychiatrist, but I'm someone who cares about you. I'm someone who cares about you. You're distracted.

By me. Why is that? What is it about me you're distracted by? Oh, I see.

Oh, this is. Yeah, well, I wasn't expecting to hear that today. I never do.

So you have a crush on me. Well, I applaud your honesty and transparency. I don't return those feelings, but.

If that's all this is, that's the only thing that's distracting you. Maybe it's one of those things that you just need to get out of your system. I mean, you know what I mean.

Just just once. I can indulge those thoughts. I'm not your teacher, like I said.

Is this unprofessional? I bet it is, but I'm not your but I'm not being held to the same standards. This would be entirely consensual by you, your choice.

You're you're able to make decisions like this. I won't retaliate in any way if you say no or if you say yes. As long as you treat me well, I can treat you all back.

And my idea of treating you well is making you pass this mathematics course. And I hope you'll share some of that passion for mathematics as I do. Well, how about I just get down below this desk? And you just open your textbook on page one, one hundred and eighty seven.

Should be some problems, some starter problems in there. I've explained to you how integrals work. You know how derivatives work.

Just apply the opposite. And how about you just solve a few and how about you just solve a few of those for me while I get ready? Hey, don't be shy.

Spread your legs for me. Show me what I've got to work with. Oh, OK.

You solve those tasks for me. Let's do five. I'll check them afterwards.

And I guess I'll give you my rating and some feedback. I guess I'll give you my rating and some feedback. Are you ready? I'm going to eat your pussy now.

Oh. Mm hmm. They're going to forget to see.

Yeah. Be a good girl for me. Mm hmm.

You done with the first one yet? Oh, you're making progress. Mm hmm.

I want you to master this. You're going to feel like, maybe you'll deserve one more of these some other day. Maybe I'll reward you.

Keep solving those integrals. And don't forget the C. Mm hmm.

Mm hmm. No. Mm hmm.

Mm hmm. Oh, let me suck on that. Oh.

Mm hmm. Mm hmm. Mm hmm.

Mm hmm. Mm hmm. Mm hmm.

Mm hmm. Mm hmm. Mm hmm.

Mm hmm. Mm hmm. Mm hmm.

How does that feel?