lrte_gui_sage.py

#1) MRG 2015.0511 LRTE with GUI input!
@interact
def lrte(f=x^2,a=1,b=5,n=slider(1,1000,1,4),method=selector(['Left','Right','Trap']),fillIt=('fill',False)):
    p=Graphics()
    h=(b-a)/n
    if method=='Left':
        l=sum([f(a+i*h)*h for i in range(n)])
        for i in range(n):
            x=a+i*h
            y=f(a+i*h)
            p+=polygon([(x,0),(x,y),(x+h,y),(x+h,0)],fill=fillIt)
        p+=plot(f,a,b,color='red',fill=True)
        p.show()
        print "l="
        print l.n(digits=6)
    if method=='Right':
        l=sum([f(a+i*h)*h for i in range(n)])
        r=l-f(a)*h+f(b)*h
        for i in range(n):
            x=a+i*h
            y=f(a+(i+1)*h)
            p+=polygon([(x,0),(x,y),(x+h,y),(x+h,0)],fill=fillIt)
        p+=plot(f,a,b,color='red',fill=True)
        p.show()
        print "[l,r]="
        print [l.n(digits=6),r.n(digits=6)]
    if method=='Trap':
        l=sum([f(a+i*h)*h for i in range(n)])
        r=sum([f(a+i*h)*h for i in range(n)])-f(a)*h+f(b)*h
        t=(r+l)/2
        e=(r-l)/2
        for i in range(n):
            x=a+i*h
            y1=f(a+i*h)
            y2=f(a+(i+1)*h)
            p+=polygon([(x,0),(x,y1),(x+h,y2),(x+h,0)],fill=fillIt)
        p+=plot(f,a,b,color='red',fill=True)
        p.show()
        print "[l,r,t,e]="
        print [l.n(digits=6),r.n(digits=6),t.n(digits=6),e.n(digits=6)]