회전체 부피, 디스크법

x = var('x') @interact def disk_vol(f = input_box(default = sqrt(1 - x^2), type = SR), Start = input_box(default = -1), End = input_box(default = 1), n=slider(4,100,4, default=16)): pretty_print(html('$$f(x) = %s$$'%latex(f))) func(x) = f a = RDF(Start) b = RDF(End) dx = (b-a)/n xpts = [a+i*dx for i in range(n+1)] ypts = [func(x=xpts[i]) for i in range(n+1)] midxs = [a+i*dx+dx/2 for i in range(n)] p=Graphics() dV = [] for i in range(0,n): dx = xpts[i+1] - xpts[i] yi = func(x=midxs[i]) p+=revolution_plot3d(yi,(x,xpts[i],xpts[i+1]), show_curve=True, opacity=0.5, parallel_axis='x') dV.append(dx*pi*yi*yi) Vn = sum(dV); Vn = RDF(Vn) V = integral(pi*func*func,x,a,b); V = RDF(V) err = abs(V - Vn) p.show(aspect_ratio=[1,1,1]) print "V =", V print "Vn = %s" %(Vn) print "Error =", err