Dtyjlui

1 Let $S$ be a surface in $mathbb{R^3} $ with the parametrization $g(s, t) = (t, t^2 , st)$ where $g : [0, 1] × [0, 10] → mathbb{R^3} $ . Explain why the area of $S$ is equal to $int_C xdσ$ , where $C$ is the curve in $mathbb{R^2}$ parameterized by $h(t) = (t, t^2 )$ , $h : [0, 10] → mathbb{R^2}$ and Find the area of $S$ . i didn't understand the question at all how can i explain that . Area $S$ = $int_C x,dsigma$ . i know that the surface area is given by : $ int f(x(t),y(t)|r'(t)| { dt}$ but the curve siting in the $[xy]$ plane is $h(t)$ so my guess (might be wrong) that $|r'(t)|$ = $sqrt{4t^2 + 1}$ and $f(x(t),y(t)) = st = sx$ . integration multivariable-calculus curvature line-integrals