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 $c∈[a,b]$ ,

$$\int_{a}^{b}{ ‍ }f\left( x \right)dx=\int_{a}^{c}{ ‍ }f\left( x \right)dx+\int_{c}^{b}{ ‍ }f\left( x \right)dx$$