Question

Verify Stokes's Theorem by evaluating F-T ds = For as a line integral and as a double integral F(x, y, z) - (-y+z)i + (x - 2)j + (x - y)k S: Z - 16 - x2 - y220 line integral double Integral I Need Help? Read it Watch Talk to a Tutor

Answer 1

F - +9+7)i + (2-7) 5 + (9-4) K S: Z = 16-22-2 , 20. 2=0, 16 = x2442 Parametric form is y = 4sine K 4 Cose J Fide Seyda ez dy) for one, 2-0, titucs 2 IT + (- 4 Sine x4 (-sine ) do 4 cos@ x4 cose do 27 52424) (sinze tegte) do 2T tida 16 0 2T 16 [o 22" 16x(2T -0) 0 E 3271 Hence, Line integral Sfidh = 32 TT Stokes' theorem we have By the F. dr ļ curli nas T Here , Cun Bay ә sz -Y+7 2-7 2-7 9-1+) 3(1-1) +(1+) 22 on the surface of the sphere 16, nê dy ŷ TzR x2 + y2 + z 2

i ScanlFinds = soffaz ds S --ff23 dady nok SS 3 32 dady 32 x area of the cincle с Curli nas 33 TT S Thus Stokes' theorem is verified. Hence, double integral, If canli ñ ds = 3275 S