Question

Let S be a surface defined by parametric equations r(u, v) = x(u, v), y(u, v), z(u, v) , for a u b and c v d. Show that the surface area of S is given by ||ru times rv||du dv, where ru (u, v) = x / u (u, v), y / u (u, v), z / u (u, v) and rv (u, v) = x / v (u, v), y / v (u, v), z / v (u, v) . Use the formula from exercise 29 to find the surface area of the surface defined by x = w, y = v + 2, z = 2uv for 0 u 2 and 0 v 1.

Show transcribed image text Let S be a surface defined by parametric equations r(u, v) = x(u, v), y(u, v), z(u, v) , for a u b and c v d. Show that the surface area of S is given by ||ru times rv||du dv, where ru (u, v) = x / u (u, v), y / u (u, v), z / u (u, v) and rv (u, v) = x / v (u, v), y / v (u, v), z / v (u, v) . Use the formula from exercise 29 to find the surface area of the surface defined by x = w, y = v + 2, z = 2uv for 0 u 2 and 0 v 1.