Need help with these 3 integrals problems

[reverie414]

URGENT !!! need help with these 3 integrals problems

Hi, I need urgent help with these 3 integrals problems ... been stuck on the questions and the deadline is Friday. Thanks a lot !

1) For the green's theorem,
>> see attach

I got the answer : 27.552. Not sure whether it is correct. Please kindly explain in steps so I know where I went wrong.


2) I'm totally unsure about finding the surface integral. How do I know the shape of the surface ?
>> see attach


3) and finding the curl function f
>> see attach

All I know is, it has something to do with curl. Something like F = grad f. How do I find the function ?


Thanks again !

 

[cristo]

You need to show your work before we can help you. For 1. a numerical answer will not help us see where/if you've gone wrong!

 

[HallsofIvy]

Hi, I need urgent help with these 3 integrals problems ... been stuck on the questions and the deadline is Friday. Thanks a lot !

1) For the green's theorem,
>> see attach

I got the answer : 27.552. Not sure whether it is correct. Please kindly explain in steps so I know where I went wrong.

No, it is not correct. I don't know what to tell you since you say nothing about what you attempted.

2) I'm totally unsure about finding the surface integral. How do I know the shape of the surface ?
>> see attach

?? Because you are TOLD the shape of the surface? What shape in x²+ y²= a²? Remember that this is in 3 dimensions. Since there is no "z" in that equation, what are the possible values for z for each (x,y)?

3) and finding the curl function f
>> see attach

All I know is, it has something to do with curl. Something like F = grad f. How do I find the function ?

The problem says specifically "Find f such that grad f= F". That has nothing to do with the curl. Are you given a specific function F? How you would do this (or even whether it is possible) depends heavily on the form of F. Notice that F has to be vector valued function and f a scalar valued function.

Please show your work and we may be able to give you some hints.

 

[reverie414]

No, it is not correct. I don't know what to tell you since you say nothing about what you attempted.



?? Because you are TOLD the shape of the surface? What shape in x²+ y²= a²? Remember that this is in 3 dimensions. Since there is no "z" in that equation, what are the possible values for z for each (x,y)?



The problem says specifically "Find f such that grad f= F". That has nothing to do with the curl. Are you given a specific function F? How you would do this (or even whether it is possible) depends heavily on the form of F. Notice that F has to be vector valued function and f a scalar valued function.

Please show your work and we may be able to give you some hints.

Hi, thanks for reply. For 2), the shape should be cylinder with radius a. I think the parametric eqn is, acos@i + asin@j + zk, 0<= @ <= 2pi, 0<= z <= h. for ru x rv = -(acos@)i - (asin@)j + (acos^2@ + asin^2@)k. Is it correct ? I need to know how to find out how to derive the magnitude and evaluate the integral. Any idea ? Thanks.

I'm still working on 3). Thanks for checking the ans for 2), I guess my working is correct.