Question

Solve:
${\int }_0^3(a{x}^2+bx+c)dx$.

Answer 1

$I={\int }_0^3(a{x}^2+bx+c)dx$
$={\begin{array}{c}(\frac{a{x}^3}{2}+\frac{b{x}^2}{2}+cx)\end{array}|}_0^3$
$=\frac{a(3{)}^3}{3}+\frac{b(3{)}^2}{2}+c\left(3\right)-0$
$=9a+\frac{9}{2}b+3c[\because {\int }_a^{b}f(x)dx=I(x){|}_a^b=I(b)-I(a\left)\right]$.