Calculate the area of the surface parameterised by

$\displaystyle r(u,v):= (\frac{1}{2}u^2,uv,v^2) $,

$\displaystyle 0 \le u \le 2, -1 \le v \le 1 $

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- Mar 11th 2011, 04:45 AMmaximus101Calculate the area of the surface parameterised form
Calculate the area of the surface parameterised by

$\displaystyle r(u,v):= (\frac{1}{2}u^2,uv,v^2) $,

$\displaystyle 0 \le u \le 2, -1 \le v \le 1 $ - Mar 11th 2011, 05:18 AMHallsofIvy
$\displaystyle r_u= (u, v, 0)$, $\displaystyle r_v= (0, u, 2v)$. The "fundamental vector product", and what you need to integrate, is the magnitude of the cross product of those two vectors, times dudv.

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