4. (20 points) Using the parametrization X(r,0) = (r cos 0,r sin 0,0) for the ry-plane in R³, it can proven

that the area of region A as it sits on the ry-plane is given by

area(4) = ₁1

1 dx dy =

||

= SS || X, X X || dr do

cos

-r sin e

It can be calculated that X, = sin 0 and X₂ = r cos 0

Find || X, X X₂ ||-

Assume r > 0. Your answer should not contain any trigonometric functions.