∫ 0 2 ( 6 x 2 − 4 x + 5 ) d x = 6 x 2 + 1 2 + 1 − 4 x 1 + 1 1 + 1 + 5 x | 0 2 = 6 x 3 3 − 4 x 2 2 + 5 x | 0 2 = 2 x 3 − 2 x 2 + 5 x | 0 2 = [ 2 ( 2 ) 3 − 2 ( 2 ) 2 + 5 ( 2 ) ] − [ 2 ( 0 ) 3 − 2 ( 0 ) 2 + 5 ( 0 ) ] = 16 − 18 + 0 = 18 {\displaystyle {\begin{aligned}\int _{0}^{2}(6x^{2}-4x+5)dx&={\frac {6x^{2+1}}{2+1}}-{\frac {4x^{1+1}}{1+1}}+{5x}{\bigg |}_{0}^{2}={\frac {6x^{3}}{3}}-{\frac {4x^{2}}{2}}+{5x}{\bigg |}_{0}^{2}=2x^{3}-2x^{2}+{5x}{\bigg |}_{0}^{2}\\[2ex]&=[2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}]=16-18+0\\[2ex]&=18\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{0}^{2}(6x^{2}-4x+5)dx&={\frac {6x^{2+1}}{2+1}}-{\frac {4x^{1+1}}{1+1}}+{5x}{\bigg |}_{0}^{2}={\frac {6x^{3}}{3}}-{\frac {4x^{2}}{2}}+{5x}{\bigg |}_{0}^{2}=2x^{3}-2x^{2}+{5x}{\bigg |}_{0}^{2}\\[2ex]&=[2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}]=16-18+0\\[2ex]&=18\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a2820a431bf7a715917f46dab4ee01aeaffb3669)