This is a manual calculation, i need you to do simulation software by using Matlab, but make sure last answer in Matlab is same answer in manual calculation please

Q4 (a) Define Gauss's theorem and Stokes' theorem. (b) Consider the outward flux of vector field, F(x, y, z) = y + xy + zk across the surfaces enclosed by cylinder x2 + y2 = 4, z= 4 plane z=0, and cone z = 7x2 + y2 (i) Sketch the graph of the surfaces. (ii) Find the divergence of F(x,y,z). (iii) Use Gauss's theorem to evaluate the flux of the vector field F(x,y,z) across the surfaces. Eo (a) Gauss's theorem states that net electric flux through closed surface is equal to total ox et charge enclosed by closed surface divided by bermittivity of medium. If electric field is present in vacuum, then mathematical equation for Gauss's theorem is &= Venclosed Here, & is net flux through closed surface, Venclosed is net charge inside closed surface and so is permittivity of medium. Stokes theorem states that "surface integral of curl of function over surface bounded by closed surface is equal to line integral of particular vector function around that surface". I Sed CS Scanjed with Cascanner S SS,F) ds 2. AS Given vector field; } = y ut ny t z Cylinder; n + y = 4, and Plane: 250 to Zz4, and come; 2= 52ty Part() zozeer yz z24 Sotetch of surfaces; + x + y=4 z = > 5 the 3 1 Z -1 -3 X 3 3 Part (11) Divergence of Pies 7.5 = F. (Jh + k g 7 + z f) Fiss FF du? tu z. F.F - Sa (y) + (27) + = (2) = 0 ++++ +1 7. F= x+1 | Divergence of E ? dy otat= c z > =r 20 2 4 Port Cos') now the Faluse using the Graues Thearoms Flur = s} F.JS = SSS (V.F) du = $35 (+2) dv wsing Cylindrical coordinates; x = ECOSO, Y = r sin 8, zzz So limit's are; osos 27C, 352, 3234 {rz= Sanaya a e} sofinally the Feluxe is; Flurez saty CaCl2 +2) 3dz dedo Eluva os "S* I s 629 6.34](434) doudo Flun os' [(4-31) s? sin@+ (491-342) 0]"der = $(250) [64-8e] do (272)52 sa? Se Jo = (27) [8_$] =) San So Finally the Filure is : z= 9 21 2 Flun = , 219 ( Flax = 2 8-8 ] 3276 3 3 3277