Show that the differential form in the integral below is exact. Then evaluate the integral. ( 5, 3, 5) I 2xdx+12ydy+82dz (0,0,0) Select the correct choice below and ll in any answer boxes within your choice. (it: A. (-5.-3.-5) I 2xdx+12ydy+82dz= (0,0,0) (Simplify your answer. Type an exact answer.) C." B. The differential form is not exact. lil Show that the differential form in the integral is exact. Then evaluate the integral. (0,3,5) sin y cos x dx + cosy sin x dy + 6 dz (1,0,0) Compute the partial derivatives. ap ON 0 dy az 0 Compute the partial derivatives. OM OP az 0 ax 0 Compute the partial derivatives. ON aM = cos y cos x ay = COS y COs X Select the correct choice below and fill in any answer boxes within your choice. (0,3,5) O A. siny cos x dx + cosysin x dy + 6 dz= (1,0,0) (Type an exact answer.) O B. The differential form is not exact.Although it is not defined on all of space R", the field associated with the line integral below is simply connected, and the component test can be used to show it is conservative. Find a potential function for the field and evaluate the integral. (4,4, 3) 1 1 ox + dy dz (2, 2,2) y A general expression for the infinitely many potential functions is f(x,y,z) = X yz Evaluate the line integral. (4,4,3) dz = 12 (2,2,2)