Problem with the region of an integral

  • Thread starter Thread starter Amaelle
  • Start date Start date
  • Tags Tags
    Integral
Amaelle
Messages
309
Reaction score
54
Homework Statement
look at the image
Relevant Equations
Stocke theorem!
Greetings!

The exercice ask to calculate the circuitation of the the vector field F on the border of the set omega
I do understand the solution very well
my problem is the region!
I m used to work with a region delimitated clearly by two intersecting function here the upper one stop a y=3 and doesn´t intersect with y=0.

thank you!
1644355492888.png
 
Physics news on Phys.org
Amaelle said:
I m used to work with a region delimitated clearly by two intersecting function here the upper one stop a y=3 and doesn´t intersect with y=0.
No, the upper function doesn't stop at y = 3. The quarter circle does, but the function is given by ##y = 3 + \sqrt{9 - x^2}##.
The region ##\Omega## is (obviously) the portion in blue. The inequality ##0 \le y \le 3 + \sqrt{9 - x^2}## includes all those y-values for which ##x \ge 0##, that run from the x-axis up to the quarter circle. For example, if x = 0, y ranges from 0 to 6; if x = 3, y ranges from 0 to 3.
 
Mark44 said:
No, the upper function doesn't stop at y = 3. The quarter circle does, but the function is given by ##y = 3 + \sqrt{9 - x^2}##.
The region ##\Omega## is (obviously) the portion in blue. The inequality ##0 \le y \le 3 + \sqrt{9 - x^2}## includes all those y-values for which ##x \ge 0##, that run from the x-axis up to the quarter circle. For example, if x = 0, y ranges from 0 to 6; if x = 3, y ranges from 0 to 3.
Thanks a million!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top