Parametrize semi-sphere equation

[rettore84]

Hello to all,

I have to calculate the line integral where the curve is a semi-sphere as shown in the image. I need some help to parametrize the semi-sphere equation.

Thank you.

 

[rettore84]

I'm still having trouble to solve this question. I know that if the curve was a circumference I would parametrize as:

x=r*cos(t)
y=r*sin(t).

If someone is able to give me some guidance I would much appreciate.

Thank you.

 

[stapel]

I have to calculate the line integral where the curve is a semi-sphere as shown in the image. I need some help to parametrize the semi-sphere equation.

I think the contents of the image are as follows:

. . . . .\(\displaystyle \displaystyle \int_A\, (2x\, +\, 2y\, +\, 2z)\, \cdot\, \eta\, ds\)

. . . . . . . . .\(\displaystyle \displaystyle A\, \longrightarrow\, x^2\, +\, y^2\, +\, z^2\, =\, 1,\, z\, >\, 0\)

. . . . . . . . .\(\displaystyle \displaystyle \eta\, \longrightarrow\, (1,\, 1\, 1)\)

If so, what do you mean by the "goes to" arrows for \(\displaystyle \, A\, \) and \(\displaystyle \, \eta ?\) Does the "dot" after the parenthetical in the integrand indicate multiplication?

Thank you!

 

[rettore84]

I think the contents of the image are as follows:

. . . . .\(\displaystyle \displaystyle \int_A\, (2x\, +\, 2y\, +\, 2z)\, \cdot\, \eta\, ds\)

. . . . . . . . .\(\displaystyle \displaystyle A\, \longrightarrow\, x^2\, +\, y^2\, +\, z^2\, =\, 1,\, z\, >\, 0\)

. . . . . . . . .\(\displaystyle \displaystyle \eta\, \longrightarrow\, (1,\, 1\, 1)\)

If so, what do you mean by the "goes to" arrows for \(\displaystyle \, A\, \) and \(\displaystyle \, \eta ?\) Does the "dot" after the parenthetical in the integrand indicate multiplication?

Thank you!

Hi Stapel thank you for your reply.

The dot is a multiplication and \(\displaystyle \, \eta \) is a unitary vector that point to the center of "A". "A" is the curve to calculate the line integral. Sorry the problem is not in English and I am trying to translate the best I can. Thank you.[FONT=MathJax_Math]η [/FONT]