3618.sagews

def LRAM(f, width, start, end):
    return width*sum(f(x) for x in [start..end-width,step=width])
def RRAM(f, width, start, end):
    return width*sum(f(x) for x in [start+width..end,step=width])

def f(x): return 1/e^x
width= 1/8
start=0
end=4

LRAM(f,width,start,end)

RRAM(f,width,start,end)

def LRAMarea(f,width,start,end):
    L=[[start,0],[start,f(start)],[start+width,f(start)],[start+width,0]]
    if start+width==end: return polygon(L)
    return polygon(L) + LRAMarea(f,width,start+width,end)
    
def RRAMarea(f,width,start,end):
    L=[[start,0],[start,f(start+width)],[start+width,f(start+width)],[start+width,0]]
    if start+width==end: return polygon(L)
    return polygon(L) + RRAMarea(f,width,start+width,end)

LRAMarea(f,width,start,end)+plot(f,(x,start,end), color='red')

RRAMarea(f,width,start,end)+plot(f,(x,start,end), color='red')

f(x) = sin(x)

@interact
def _(width=pi/12,start=0,end=pi,RAM=['None','Left','Right']):
    show(f)
    graph = plot(f,(x,start,end), color='red')
    if RAM == 'Left': 
        graph += LRAMarea(f,width,start,end)
        print 'Approximate area:',LRAM(f,width,start,end).n()
    elif RAM == 'Right': 
        graph += RRAMarea(f,width,start,end)
        print 'Approximate area:',RRAM(f,width,start,end).n()
    if RAM != 'None': print 'Actual area:',integral(f,x,start,end).n()
    show(graph,aspect_ratio=1)

width  start  end  RAM  [removed] [removed] [removed] [removed]