Definite integrals, rules
Summary
- Integral of a constant. For any constant ,
\[\int_{a}^{b}{ }kdx=k\left( b-a \right)\]
- Constant law. For any constant \(k\) ,
\[\int_{a}^{b}{ }kf\left( x \right)dx=k\int_{a}^{b}{ }f\left( x \right)dx\]
- Addition law,
\[\int_{a}^{b}{ }\left( f\left( x \right)+g\left( x \right) \right)dx=\int_{a}^{b}{ }f\left( x \right)dx+\int_{a}^{b}{ }g\left( x \right)dx\]
- Domain law. For any \(c∈[a,b]\) ,
\[\int_{a}^{b}{ }f\left( x \right)dx=\int_{a}^{c}{ }f\left( x \right)dx+\int_{c}^{b}{ }f\left( x \right)dx\]