I got this question:
Evaluate the volume V of the solid Ω that lies under the paraboloid z = x^2+y^2 , and above the circular region in the xy−plane x^2 + y^2 = 2x. Sketch the given solid.
This is what I have done, I do not know how to erase the extra part so that I can get the solid satisfying the question. Can anyone help me solving this issue?
Thank you for reading.
%Calculation
syms r phifunc = r.^3;rmax = 2.*cos(phi);result = int(int(func, 0, rmax), 0, 2*pi);disp('Result: '), disp(result);%draw the paraboloid
phi = linspace (0, 2*pi, 30);r = linspace(0, 2, 30);[r, p] = meshgrid(r, phi);x = r.*cos(p);y = r.*sin(p);z = x.^2 + y.^2;surf(x, y, z, 'FaceColor', 'g', 'FaceAlpha', 0.3);hold on%draw the cylinder
x1 = linspace(0, 2, 500); z1 = linspace(0, 4, 500);[x1,z1] = meshgrid(x1,z1);y1 = sqrt(-x1.^2 + 2.*x1);y2 = -sqrt(-x1.^2 + 2.*x1);surf(x1, real(y1), z1,'FaceColor','b','FaceAlpha',0.5,'EdgeColor','none'); %real for drawing complex number
hold on;surf(x1, real(y2), z1,'FaceColor','b','FaceAlpha',0.5,'EdgeColor','none');hold on;xlabel('x');ylabel('y');zlabel('z');rotate3d on
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