project4

# project4 - close all clear all clc%question1%a syms r s x y...

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close all; clear all, clc; %question1 %a). syms r s x y x = r*cos(s); y = r*sin(s); z = x.^2+3*y.^2+4 z = r^2*cos(s)^2 + 3*r^2*sin(s)^2 + 4 ezsurf(x,y,z,[0,1],[0,2*pi]);hold on; x = cos(s); y = sin(s); z=z; ezsurf(x,y,z,[0,1],[0,2*pi]);hold off;

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%b) volume = int(int(x.^2+3*y.^2+4,y,(-sqrt(1-x.^2)),(sqrt(1-x.^2))),x,- 1,1) volume = 5*pi %c) x = r*cos(s); y = r*sin(s); volume = int(int(r^3+2*r^3*(sin(s))^2+4*r,r,0,1),s,0,2*pi) volume = 5*pi %d) syms x y z r s volume = int(int(int(r,z,0,r^2+2*r^2*(sin(s))^2+4),r,0,1),s,0,2*pi) volume = 5*pi %2 syms u v x y z real x = (cos(u)).^3*(cos(v)).^3; y = (sin(u)).^3*(cos(v)).^3; z = (sin(v)).^3; r = [x,y,z]; ru = diff(r,u) r=r r = [ cos(u)^3*cos(v)^3, cos(v)^3*sin(u)^3, sin(v)^3] ru = [ (-3)*cos(u)^2*cos(v)^3*sin(u), 3*cos(u)*cos(v)^3*sin(u)^2, 0]
rv = diff(r,v) rv = [ (-3)*cos(u)^3*cos(v)^2*sin(v), (-3)*cos(v)^2*sin(u)^3*sin(v), 3*cos(v)*sin(v)^2] rurv = cross(ru,rv) rurv = [ 9*cos(u)*cos(v)^4*sin(u)^2*sin(v)^2, 9*cos(u)^2*cos(v)^4*sin(u)*sin(v)^2,

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project4 - close all clear all clc%question1%a syms r s x y...

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