- $ \\\int\\\limits_a^b {k.f\\\left( x \\\right)dx} = k\\\int\\\limits_a^b {f\\\left( x \\\right)dx} ,k \\\in \\\mathbb{R}$.
- $ \\\int\\\limits_a^b {\\\left[ {f\\\left( x \\\right) + g\\\left( x \\\right)} \\\right]dx} = \\\int\\\limits_a^b {f\\\left( x \\\right)dx} + \\\int\\\limits_a^b {g\\\left( x \\\right)dx}$ .
- $ \\\int\\\limits_b^a {f\\\left( x \\\right)dx} = - \\\int\\\limits_a^b {f\\\left( x \\\right)} dx$.
- $ \\\int\\\limits_a^b {\\\left[ {f\\\left( x \\\right).g\\\left( x \\\right)} \\\right]dx} = \\\int\\\limits_a^b {f\\\left( x \\\right)dx} .\\\int\\\limits_a^b {g\\\left( x \\\right)dx}$ .