Home/Calculus II/Improper integrals/ComparisonSection 9.4ComparisonIf 0≤f(x)≤g(x)0\le f(x)\le g(x)0≤f(x)≤g(x) for xxx sufficiently large:#If ∫g\int g∫g converges, then ∫f\int f∫f converges.If ∫f\int f∫f diverges, then ∫g\int g∫g diverges.Limit comparison: ifFormulaCopy LaTeXlimx→∞f(x)g(x)=L,0<L<∞,\lim_{x\to\infty}\frac{f(x)}{g(x)}=L, \qquad 0<L<\infty,x→∞limg(x)f(x)=L,0<L<∞,0<L<∞,0<L<\infty,0<L<∞,View detail →then ∫f\int f∫f and ∫g\int g∫g have the same behavior.
FormulaCopy LaTeXlimx→∞f(x)g(x)=L,0<L<∞,\lim_{x\to\infty}\frac{f(x)}{g(x)}=L, \qquad 0<L<\infty,x→∞limg(x)f(x)=L,0<L<∞,0<L<∞,0<L<\infty,0<L<∞,View detail →