Improper Integrals

examples

>	with(plots):

Warning, the name changecoords has been redefined

Section 8.8#16

>	Int(5/x^3,x=1..infinity);

>

value(%);

>	plot(5/x^3,x=1..5,filled=true);

>	plot(5/x^3,x=1..100,filled=true);

Section 8.8#20

>	Int(x*exp(-x/2),x=0..infinity);

>

value(%);

>	plot(x*exp(-x/2),x=0..10,filled=true);

>	plot(x*exp(-x/2),x=0..100,filled=true);

Section 8.8#26

>	Int(ln(x)/x,x=1..infinity);

>

value(%);

>	plot(ln(x)/x,x=1..100,filled=true);

Section 8.8#30

>	Int(exp(x)/(1+exp(x)),x=0..infinity);

>

value(%);

>	plot(exp(x)/(1+exp(x)),x=0..20,filled=true);

Section 8.8#34

>	Int(8/x,x=0..4);

>

value(%);

>	plot(8/x,x=0..4,y=0..100,filled=true);

Section 8.8#36

>	Int(4/sqrt(6-x),x=0..6);

>

value(%);

>	plot(4/sqrt(6-x),x=0..6,y=0..30,filled=true);

Section 8.8#38

>	Int(ln(x^2),x=0..exp(1));

>

value(%);

>	plot(ln(x^2),x=0..exp(1),filled=true);

Section 8.8#48

>	Int(1/(x*ln(x)),x=1..infinity);

>

value(%);

>	plot(1/(x*ln(x)),x=1..6,y=0..20,filled=true);

>	Int(1/(x^2+1),x=-infinity..infinity);

>

value(%);

>	plot(1/(x^2+1),x=-10..10,filled=true);

>