Question

line.. Cl UL UDCITTugu Math & Stats for Aero, Mech & Auto (MATH2124 1910) Student Test Page- Multivariable Learn // Calculus 5 Question Question 11 (2 marks) Attempt 5 S is the half cylinder2+y2-9, y> 0, 0<z <3 Given the vector field: E=(20+7yz)i+(9z2+72) j+(2x2z-723)k, Calculate the outward flux (away from the z-axis) of E through surface S. That is find E-dS Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 J =

Answer 1

Sx 9, y2 0,0ss3 + xz-plane Dx,-):-3 sxs3,0 ss3} +7:)j+(2x2:-7 :)k then Vf-2xi + 2y Projection of E on E(2x+7yz)i+(9 Letf(x, y.)x y Now, 7y2)+(9+ 7=)j+ (2x -7' ) ] E ds d4 |k I(2x+7y)i+(92+7)j+(2x: - 72 ) k] (2xi+2v)d4 2x(2x+ 7yz)+2y(92 +7)d4 2x27x19-xz+9/9-x22+79-x2 dzc 7x9 9 6x7x9- +3x279-x dx + X X 2 75 21 2x+ 2 9-xdx -2x3 75 2x 0+ 2 As x9-x dx is an odd function 75 2x + 2x33 75 9T + x 2 6x3 3 4 6075T =324+ 4 Il