Calculus UNIT507a: Riemann Sums with GUI input!

2404 days ago by MATH4R2013

#1) MRG LRTE! @interact def lrte(f=x^2,a=1,b=5,n=slider(1,10,1,4),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)] 
       
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