3. Computation Rules

Sum Rule

${\int }_a^b(f(x)+g(x))dx={\int }_a^{b}f(x)dx+{\int }_a^{b}g(x)dx$

Scalar Multiplication Rule

${\int }_a^{b}cf(x)dx=c{\int }_a^{b}f(x)dx$

Difference Rule

${\int }_a^b(f(x)-g(x))dx={\int }_a^{b}f(x)dx-{\int }_a^{b}g(x)dx$

Union of Intervals

${\int }_a^{b}f(x)dx+{\int }_b^{c}f(x)dx={\int }_a^{c}f(x)dx$

Comparison Rule

${\int }_a^{b}f(x)dx\le {\int }_a^{b}g(x)dx$

if $f(x)\le g(x)$ for all $x$ in the interval $(a,b)$