More Improper Integrals

examples

>	with(plots):

Warning, the name changecoords has been redefined

Section8.8#48

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

>

value(%);

>	plot(1/(x*ln(x)),x=1..5,y=0..30,filled=true);

Section 8.8#69

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

>

value(%);

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

Section 8.8#73

We need the following command to avoid Maple evaluating an expression in terms of non-real complex numbers and as a result constructing an incomplete graph.

>	with(RealDomain):

Warning, these protected names have been redefined and unprotected: Im, Re, ^, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, cos, cosh, cot, coth, csc, csch, eval, exp, expand, limit, ln, log, sec, sech, signum, simplify, sin, sinh, solve, sqrt, surd, tan, tanh

>	implicitplot(x^(2/3)+y^(2/3)=4,x=-9..9,y=-9..9,thickness=3,numpoints=2500);

>	4*Int(2*x^(-1/3),x=0..8);

>

value(%);

>