Quick refresher - integral calculus

[Howard]

S(C(R^2 - r^2) 2pi*r dr)
so that becomes

2*pi*C*S(r(R^2 - r^2)dr)

R is a constant. Any ideas?

 

[BrownTown]

http://integrals.wolfram.com/index.jsp

 

[Random Variable]

I would help you if I understood your notation.

Is S supposed to be an integral sign? And is C another constant?

 

[Howard]

S is the integral sign, summa

 

[Howard]

OK, now I feel like an idiot.

I hate forgetting elementary stuff, but more than that, I hate having to remember it. Damn fluid mechanics.

 

[Random Variable]

let u= R^2-r^2
then du = -2rdr

 

[Howard]

Couldn't you just expand the brackets and integrate each term?

 

[Random Variable]

Originally posted by: Howard
Couldn't you just expand the brackets and integrate each term?

yes

 

[Howard]

http://psu.thetruck.net/Chapter%203%20solutions.pdf

1st question. I can't get the same answer.

ugh, i'm fvcked for this chapter.

 

[Random Variable]

let u = R^2-r^2
then du = -2rdr

-Pi*C?udu = -Pi*C*u^2/2 = -Pi/2*C*(R^2-r^2)^2

now evaluate it at the limits

-Pi/2*C*[0-R^2]^2 = Pi/2*C*R^4

 

[Howard]

oh, right

I'm screwed

 

[Random Variable]

Originally posted by: Howard
oh, right

I'm screwed

You can't follow what I did? It's really quite a simple integral.

 

[Howard]

No, I can follow it, but I can't do integrals like I used to.

 

[Random Variable]

I'm fairly certain that in a fluid dynamics course you're going to come across all kinds of integrals.

particularly surface integrals