parameterization

**calc626** · November 11th 2009, 02:55 PM

a parameterization for a surface called a helicoid is given: f(s,t)= (scost,ssint,t)

compute the surface area of the helicoid corresponding to (s,t): [0,1]x[0,2pi]

sorry i'm completely lost on this problem..any ideas how to set it up?

**Danny** · November 11th 2009, 04:01 PM

Originally Posted by calc626

a parameterization for a surface called a helicoid is given: f(s,t)= (scost,ssint,t)

compute the surface area of the helicoid corresponding to (s,t): [0,1]x[0,2pi]

sorry i'm completely lost on this problem..any ideas how to set it up?

Usually we have the surface given parametrically as

$<br /> {\bf r} = {\bf r}(u,v)<br />$

and the surface area is given by

$\iint_R || {\bf r_u \times r_v } || dA\,\, (1)$

Here, we have

$<br /> {\bf f} = < s \cos t,s \sin t,t><br />$

so identify ${\bf r = f},\;\;u = s$ and $v = t$ and follow (1)

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