- #1
Smusko
- 20
- 0
I will denote vectors in bold.
Show that the curve C given by
r=a*Cos(t)Sin(t)i+a*Sin2(t)j+a*Cos(t)k ( 0=<t=<pi/2 )
lies on a sphere centred at the origin.
Find [tex]\int zdS[/tex] under C
*edit* There is a huge gap here and the equation has dissapered for me. But what it said was Integral(zdS) under C
The solution is (a2/2)*(sqrt(2)+ln(1+sqrt(2))
To show that the curve was on a sphere centred at the origin I just put in various values for t onto the curve and plotted it onto a graph.
Maybe there's a way to do it algebraically. But that is not the part I'm looking for help with.
I want help figuring out what to do with the Z in the integral and calculating it.
I got dS = |dr / dt|*dt = a*cos(t)dt
I am totally lost how to parametrize Z or figuring out the domain. The book I use gives no clear example on what to do, or it is just wooshing over my head.
I have tried grasping straws but nothing comes close to the answer given by the solution section.
Help is much appreciated. :)
*edit*
Latex seems to be totally bugging out on me. Weird suff shows up when I refresh, Stuff I have edited away keeps coming back, and now there is a huge gap in the post. Tell me if you see the same thing or if its just me.
Homework Statement
Show that the curve C given by
r=a*Cos(t)Sin(t)i+a*Sin2(t)j+a*Cos(t)k ( 0=<t=<pi/2 )
lies on a sphere centred at the origin.
Find [tex]\int zdS[/tex] under C
*edit* There is a huge gap here and the equation has dissapered for me. But what it said was Integral(zdS) under C
Homework Equations
The solution is (a2/2)*(sqrt(2)+ln(1+sqrt(2))
The Attempt at a Solution
To show that the curve was on a sphere centred at the origin I just put in various values for t onto the curve and plotted it onto a graph.
Maybe there's a way to do it algebraically. But that is not the part I'm looking for help with.
I want help figuring out what to do with the Z in the integral and calculating it.
I got dS = |dr / dt|*dt = a*cos(t)dt
I am totally lost how to parametrize Z or figuring out the domain. The book I use gives no clear example on what to do, or it is just wooshing over my head.
I have tried grasping straws but nothing comes close to the answer given by the solution section.
Help is much appreciated. :)
*edit*
Latex seems to be totally bugging out on me. Weird suff shows up when I refresh, Stuff I have edited away keeps coming back, and now there is a huge gap in the post. Tell me if you see the same thing or if its just me.
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