Evaluate the surfacuse stokes's theorem to evaluate f · dr c. use a computer algebra system to verify your results. in this case, c is oriented counterclockwise as viewed from above. f(x, y, z) = 2yi + 3zj + xk c. triangle with vertices (5, 0, 0), (0, 5, 0), (0, 0, 5)e integral (x^2+y^2+z^2)ds

Since you're asked to use Stoke's theorem, I'm interpreting the question to be asking to compute the line integral



which by Stoke's theorem is equivalent to the surface integral



where is the positively-oriented surface with boundary .

Given , we get curl



We parameterize the surface by



with and . Then we take the partial derivatives of and check their cross product:



Now,



so the surface integral reduces to