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with(plots):
a:=1:b:=10:c:=0:d:=1:K:=100:
f:=x->1/(2*x):
quxian:=plot(f(x),x=0.5..b,view=[0.5..b,c..d],thickness=3):
mianji:=seq(plot([x,f(x),x=a..a+(b-a)*k/K],filled=true,color=green),k=1..K):
mianji:=display(mianji,insequence=true):
ta:=textplot([a-0.05,0,"a "],align=BELOW):
tb:=seq(textplot([a+(b-a)*i/K,-0.05,"b "],align=BELOW),i=1..K):
tb:=display(tb,insequence=true):
Line:=seq(plot([[a+(b-a)*i/K,-0.05],[a+(b-a)*i/K,f(a+(b-a)*i/K)]],linestyle=2,color=black),i=1..K):
Line:=display(Line,insequence=true):
Ab:=seq(textplot([a+((b-a)*i/K)/2,f(a+((b-a)*i/K)/2)/2,"A(b)"]),i=1..K):
Ab:=display(Ab,insequence=true):
display(quxian,mianji,ta,tb,Line,Ab,tickmarks=[0,0],view=[0..b,c..d],title="Improper Integral");

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with(plots):
a:=-6:b:=-1:K:=100:
f:=x->1/x^2:
quxian:=plot(f(x),x=a..b,thickness=3):
mianji:=seq(plot([x,f(x),x=b..b-(b-a)*k/K],filled=true,color=green),k=1..K):
mianji:=display(mianji,insequence=true):
tb:=textplot([b-0.05,0,"b "],align=BELOW):
ta:=seq(textplot([b-(b-a)*i/K,-0.05,"a "],align=BELOW),i=1..K):
ta:=display(ta,insequence=true):
Line:=seq(plot([[b-(b-a)*i/K,-0.05],[b-(b-a)*i/K,f(b-(b-a)*i/K)]],color=blue),i=1..K):
Line:=display(Line,insequence=true):
Ab:=seq(textplot([b-((b-a)*i/K)/2,f(b-((b-a)*i/K)/2)/2,"A(a)"]),i=1..K):
Ab:=display(Ab,insequence=true):
display(quxian,mianji,ta,tb,Line,Ab,tickmarks=[0,0],view=[a..b,0..1],title="Improper Integral");

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with(plots):
a:=0:b:=20:c:=-1:d:=1:K:=100:
f:=x->cos(x):
quxian:=plot(f(x),x=a..b,view=[a..b,c..d],thickness=3):
mianji:=seq(plot([x,f(x),x=a..a+(b-a)*k/K],filled=true,color=green),k=1..K):
mianji:=display(mianji,insequence=true):
tb:=seq(textplot([a+(b-a)*i/K,-0.05,"b "],align=BELOW),i=1..K):
tb:=display(tb,insequence=true):
Line:=seq(plot([[a+(b-a)*i/K,-0.05],[a+(b-a)*i/K,f(a+(b-a)*i/K)]],linestyle=2,color=black),i=1..K):
Line:=display(Line,insequence=true):
display(quxian,mianji,tb,Line,tickmarks=[4,2],view=[0..b,c..d],title="y=cos(x)",scaling=unconstrained);