\(\displaystyle \int_a^bf(x)dx=F(x)|_a^b=F(b) - F(a),\)
\(F'(x)=f(x)\)
\((f(x) \pm g(x))dx=\displaystyle \int_a^bf(x)dx \pm \displaystyle \int_a^bg(x)dx\)
\(\displaystyle \int_a^b Cf(x)dx = C \displaystyle \int_a^bf(x)dx\)
\(\displaystyle \int_a^a f(x)dx = 0\)
\(\displaystyle \int_a^b f(x)dx = - \displaystyle \int_b^af(x)dx\)
\(\displaystyle \int_a^b f(x)dx = \displaystyle \int_a^cf(x)dx + \displaystyle \int_c^bf(x)dx\)
\(\displaystyle \int_a^b f(x)dx = (b-a)f(c), a \leq c \leq b\)
\(\displaystyle \int_a^b f(x)g(x)dx = f(c) \displaystyle \int_a^b g(x)dx, a \leq c \leq b, g(x)\ge0.\)
Copyright © 2021 HOCTAPSGK