Area between Curves: Calculus Solution

[Sirsh]

Hello all.

This is not homework, i stumbled upon it looking for information for my physics.. I have some background in calculus and am just wondering if anyone would have any idea on how you'd solve this area problem.. all i have is a picture of it and not any equations of the lines.

Thanks.

 

[berkeman]

Hello all.

This is not homework, i stumbled upon it looking for information for my physics.. I have some background in calculus and am just wondering if anyone would have any idea on how you'd solve this area problem.. all i have is a picture of it and not any equations of the lines.

Thanks.

Sure. Print it, cut out the area, weigh the paper cutout (and weigh a full piece of paper with known dimensions). I still remember my undergrad Physics TA telling me about this technique...

 

[berkeman]

Oh, and what is the context of the question?

 

[Sirsh]

Wow that's a very smart idea haha. Um, it was just finding out the way to calculate the area of the region D. Is there anyway mathmatically?

My thoughts are to take away the area of C1 from a-b from the area of C3 from a-b with integration.

 

[berkeman]

Wow that's a very smart idea haha. Um, it was just finding out the way to calculate the area of the region D. Is there anyway mathmatically?

My thoughts are to take away the area of C1 from a-b from the area of C3 from a-b with integration.

You said you had no equations. What do you plan to integrate?

 

[Mark44]

I notice that the curves that bound the region are marked with arrows. Is this some kind of a path integral? I seem to remember that the line integral along a closed path in a conservative field is zero.

 

[Sirsh]

Ah yes, i don't my msitake.

http://en.wikipedia.org/wiki/Green's_theorem

That's the webpage I got the picture from..

 

[Mark44]

Ah yes, i don't my msitake.

? What are you saying here?

http://en.wikipedia.org/wiki/Green's_theorem

That's the webpage I got the picture from..