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Multivariable Calculus

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Surface Area Element of Implicit Equation

MVCALC-DREKYE

Determine the area element $dS$ for the surface given parametrically by:

$$\Phi(u,v)=\langle u\cos v, u\sin v, \frac{1}{2}u^2\sin^2 v\rangle, u>0, v>0$$

A

$dS=u(u^2 \cos^2 v + 1) dudv$

B

$dS=(4u^2 \cos^2 v + 1) dudv$

C

$dS=u\sqrt{u^2 \sin^2 v + 1} dudv$

D

$dS=u\sqrt{u^2 \cos^2 v + 1} dudv$

E

$dS=u\sqrt{4u^2 \cos^2 v + 1} dudv$