Use Stoke's theorem to evaluate ?

[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 1133 in chapter 15.8 in the text, number 14. It reads:

 

Use Stoke's theorem to evaluate Integral (with C at bottom) of F (with a dot) dr

It states that in each case, C is oriented counterclockwise as viewed from above.

For this specific problem is gives,

F(x,y,z)=4xzi + yj + 4xyk

and

S: z= 9-x^2-y^2

and z>=0

 

Again, i literally haven't a clue where to go with these =/ I looked at the soln's to the other problems in this set but still haven't a clue where to go! =/

Any help at all would be greatly appreciated. Thanks guys

[Klaynos]

Stokes theorem is another standard convert one type of integral to another that is used quite often:

 

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

 

This normally makes the integral easier, depending on which way you go, some functions are easier in one form compared to the other.