from sage.symbolic.integration.integral import definite_integral
var('x,y'); f1,f2=2^x,2*x-x^2; x1,x2=0,2; y1,y2=0,4; d=1 s=definite_integral(f1-f2,x,x1,x2)
l=[[0,0]]+[[.01*i,f1(x=.01*i)] for i in range(200)]+\
[[2,0]]+[[.01*i,f2(x=.01*i)] for i in range(200,0,-1)]
st=r'<left><font>$\displaystyle{S = %s = %s}$</font></left>'pretty_print(html(st%(str(s),str(s.n()))))
p1=plot([f1,f2],(x,x1,x2),fill={0:[1]},thickness=3, fillcolor='#3636ff',color='silver')
p2=region_plot([y-f1<0,y-f2>0],(x,x1,x2),(y,y1,y2),
alpha=.5,incol='#3636ff',
borderwidth=3,bordercol='silver')
p3=polygon2d(l,color='#3636ff',edgecolor='silver',
g=graphics_array((p1,p2,p3))
g.show(xmin=x1-d,xmax=x2+d,ymin=y1-d,ymax=y2+d,
figsize=6,aspect_ratio=1)
definite_integral(f1-f2,x,x1,x2).n()==\
(definite_integral(f1,x,x1,x2)-definite_integral(f2,x,x1,x2)).n()
No comments:
Post a Comment