Use Green's theorem to calculate work done ?

[CalleighMay]

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help!

 

I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P

 

Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help?

 

We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book.

 

The problem is on pg 1096 in chapter 15.4 in the text, number 24. It reads:

 

Use green's theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C

It gives:

F(x,y)=(3x^2+y)i + 4xy^2j

and gives:

C: boundary of the region lying between the graphs of y=(sqrt x) and y=0, and x=9

 

I looked at similar problems in the same section and came up with the following for this one:

 

work= integral (with C at bottom) of 3x^2+y dx + 4xy^2 dy

=Integral (with R at bottom) of the integral of ?

..this is where i get lost, kind of confused as to what the C is and how to integrate with it. Also, what's R?

 

This doesn't seem that bad of a problem, i just think i'm missing something since it seems too easy?

 

Any further help would be greatly appreciated. Thanks guys!! =/

[Klaynos]

C is probably meaning line integral (circumference), and R is probably meaning a surface integral (Area).

 

Green's theorem is a standard method for converting integrals from one type to another:

 

http://mathworld.wolfram.com/GreensTheorem.html