अनन्त समाकल

अनंत समाकल (improper integral या infinite integral) निम्नलिखित प्रकार के होते हैं- lim b → ∞ ∫ a b f ( x ) d x , lim a → − ∞ ∫ a b f ( x ) d x , {\displaystyle \lim _{b\to \infty }\int _{a}^{b}f(x)\,\mathrm {d} x,\qquad \lim _{a\to -\infty }\int _{a}^{b}f(x)\,\mathrm {d} x,} or of the form lim c → b − ∫ a c f ( x ) d x , lim c → a + ∫ c b f ( x ) d x , {\displaystyle \lim _{c\to b^{-}}\int _{a}^{c}f(x)\,\mathrm {d} x,\quad \lim _{c\to a^{+}}\int _{c}^{b}f(x)\,\mathrm {d} x,} == उदाहरण == ∫ 1 ∞ 1 x 2 d x = lim b → ∞ ∫ 1 b 1 x 2 d x = lim b → ∞ ( − 1 b + 1 1 ) = 1. {\displaystyle \int _{1}^{\infty }{\frac {1}{x^{2}}}\,\mathrm {d} x=\lim _{b\to \infty }\int _{1}^{b}{\frac {1}{x^{2}}}\,\mathrm {d} x=\lim _{b\to \infty }\left(-{\frac {1}{b}}+{\frac {1}{1}}\right)=1.}