5.4 Indefinite Integrals and the Net Change Theorem/21: Difference between revisions
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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>\frac{6x^{3}}{3}-\frac{4x^{2}}{2}+{5x}\bigg|_{0}^{2}</math> = <math>2x^{3}-2x^{2}+{5x}\bigg|_{0}^{2}</math> = <math>[2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}\bigg|_{0}^{2}]</math> = <math>16-18+0</math> = <math>18</math> | <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>\frac{6x^{3}}{3}-\frac{4x^{2}}{2}+{5x}\bigg|_{0}^{2}</math> = <math>2x^{3}-2x^{2}+{5x}\bigg|_{0}^{2}</math> | |||
&= <math>[2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}\bigg|_{0}^{2}]</math> = <math>16-18+0</math> | |||
&= <math>18</math> | |||
Revision as of 19:21, 30 August 2022
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![{\displaystyle [2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}{\bigg |}_{0}^{2}]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/e6b261a5c8ef3236c47bc8332c80b70a53feb993)
