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| <math>\int_{0}^{2}(6x^{2}-4x+5) dx</math> = <math>\frac{6x^{2+1}}{2+1}-\frac{4x^{1+1}}{1+1}+{5x}\bigg|_{0}^{2}</math> | | <math>\begin{align}\int_{0}^{2}(6x^{2}-4x+5) dx = \frac{6x^{2+1}}{2+1}-\frac{4x^{1+1}}{1+1}+{5x}\bigg|_{0}^{2} |
| = <math>\frac{6x^{3}}{3}-\frac{4x^{2}}{2}+{5x}\bigg|_{0}^{2}</math> = <math>2x^{3}-2x^{2}+{5x}\bigg|_{0}^{2}</math> | | =\frac{6x^{3}}{3}-\frac{4x^{2}}{2}+{5x}\bigg|_{0}^{2} = 2x^{3}-2x^{2}+{5x}\bigg|_{0}^{2} |
| = <math>[2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}]</math> = <math>16-18+0</math> | | = [2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}] = 16-18+0 |
| = <math>18</math> | | = 18\end{align}</math> |
Revision as of 19:24, 30 August 2022
![{\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}=[2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}]=16-18+0=18\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/0f51f275fb7787ee8eb539a8b7501e02112a7f32)