We'll do is essentially try to express ds right over The parametrization, let's try to evaluate It might be helpful to review Sal's videos on parameterization: NB: if you replace x with u and y with (v²) in the equation for r, then you would need to find the z above the point x=u, y=v² on the x-y plane which would be z = u + (v²)² Move z units parallel to the z-axis (where z = x + y²) Thus, to reach any point from the origin you can do the following: In other words, each point in the x-y plane maps onto the surface and the height of that surface above the x-y plane will be x + y². You can think of this as z being a function in terms of x and y - z(x,y) = x + y². The formula for the coordinates of each point on the surface is z = x + y². (note that I've not used u and v since they are exactly equivalent to x and y) it is a vector from the origin to each point on the surface S
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