Updates

MATLAB/Area/Area between curves/Area bounded by curves of form x = f(y)/code.m

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+clear
+clc
+syms y
+f = input("Enter right curve f(y): ");
+g = input("Enter left curve f(y): ");
+L = input("Enter limits of integration: [a,b]: ");
+a = L(1);b = L(2);
+Area = int(f-g,y,a,b);
+disp(Area);
+y1 = linspace(a,b,20);x1 = subs(f,y,y1);
+y2 = y1;x2 = subs(g,y,y2);
+plot(x1,y1);hold on;plot(x2,y2);hold off;
+xlabel('x-axis');ylabel('y-axis');
+legend('f(x)','g(x)');grid on;

MATLAB/Area/Area between curves/Area bounded by curves of form y = f(x)/code.m

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+clear all
+clc
+syms x
+f = input("Enter the upper curve f(x): ");
+g = input("Enter the lower curve g(x): ");
+L = input("Enter the limits of integration for x [a,b]: ");
+a = L(1);b = L(2);
+x1 = linspace(a,b,20);y1 = subs(f,x,x1);
+x2 = x1;y2 = subs(g,x,x2);
+Area = int(f-g,x,a,b);
+disp(['Area bounded by the curves f(x) and g(x) is ',char(Area)])
+plot(x1,y1);hold on;plot(x2,y2);hold off;
+xlabel('x-axis');ylabel('y-label');
+legend('f(x)','g(x)');grid on;

MATLAB/Area/Area under the curve/Area under a curve between two values of x and x-axis/code.m

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+clear
+clc
+syms x
+f = input('Enter curve f(x): ');
+L = input('Enter limits [a,b]: ');
+a = L(1);b=L(2);
+Area = int(abs(f),x,a,b);
+disp("The area is: ")
+disp(Area)
+x1 = linspace(a,b,20);y1 = subs(f,x,x1);
+plot(x1,y1);
+xlabel('x-axis');ylabel('y-label');
+legend('f(x)');grid on;

MATLAB/Volume/Solids of Revolution/Revolving a curve y = x^(1/2) about line y=1 from x=1 to x=4/code.m

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+% Evaluation of Volume of solid of revolution
+clear
+clc
+syms x
+f(x)=sqrt(x); % Given function
+yr=1; % Axis of revolution y=yr
+I=[0,4]; % Interval of integration
+a=I(1);b=I(2);
+vol=pi*int((f(x)-yr)^2,a,b);
+disp('Volume of solid of revolution is: ');
+disp(vol); % Visualization if solid of revolution
+fx=matlabFunction(f);
+xv = linspace(a,b,101); % Creates 101 points from a to b
+[X,Y,Z] = cylinder(fx(xv)-yr);
+Z = a+Z.*(b-a); % Extending the default unit height of the
+% cylinder profile to the interval of integration
+surf(Z,Y+yr,X) % Plotting the solid of revolution about y=yr
+hold on;
+plot([a b],[yr yr],'-r','LineWidth',2); % Plotting the line y=yr
+view(22,11); % 3-D graph viewpoint specification
+xlabel('X-axis');ylabel('Y-axis');zlabel('Z-axis');