Incomplete integration explanation

[BOAS]

hello,

i have a question about an explanation of integration as finding the area under a curve. I don't have any problems doing the integration but it's more a case of why?

Finding the area bound by two curves is easy enough but what does that area actually mean?

I know that it's a useful tool applied to physical examples where the area under the curve of something like radioactive decay has units, but I don't understand what it means to speak of area without giving it some units.

I hope that makes sense and that I have posted this in a relevant subsection. I don't know if it's a useful question to ask, but if there is an answer out there, I would be interested to know.

Thanks,

BOAS

 

[tiny-tim]

Hi BOAS!

Suppose you have a graph of force against time, for when a bat hits a ball.

The area under the curve is the total momentum imparted to the ball.

(and it equals ∫ F dt, which comes from F = d(momentum)/dt)

 

[BOAS]

Hi BOAS!

Suppose you have a graph of force against time, for when a bat hits a ball.

The area under the curve is the total momentum imparted to the ball.

(and it equals ∫ F dt, which comes from F = d(momentum)/dt)

Hello,

thanks for the response.

I do appreciate that integration as a method for finding the area beneath a curve is an extremely useful tool. What is bugging me a little, is the idea of finding the area bound by say, two curves. It doesn't seem meaningful to speak of area without units, although a quick sketch of the curve will tell you that there is indeed an area there.

It isn't really a big deal, but "area = 4" just feels odd and I was wondering if there was some explanation of why it can make sense without needing any units.

 

[tiny-tim]

Hello BOAS!

What is bugging me a little, is the idea of finding the area bound by say, two curves. It doesn't seem meaningful to speak of area without units, although a quick sketch of the curve will tell you that there is indeed an area there.

… why it can make sense without needing any units.

there are units …

eg in my example, the axes had units of Newtons and seconds, with an area of Newton-seconds

(and for an example of what an area-bounded-by-two-curves can represent, see http://en.wikipedia.org/wiki/Hysteresis )

 

[BOAS]

Hello BOAS!


there are units …

eg in my example, the axes had units of Newtons and seconds, with an area of Newton-seconds

(and for an example of what an area-bounded-by-two-curves can represent, see http://en.wikipedia.org/wiki/Hysteresis )

I do understand your example - I think I'm splitting hairs really.

In my maths class we've been doing problems that don't represent any physical thing, so neither axis had units.

I don't think it's especially important, I was just curious to see if there was a mathematical reason for being able to talk about are without units.