5.3 The Fundamental Theorem of Calculus/27: Difference between revisions
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\begin{align} | \begin{align} | ||
\int_2^0 x(2+x^5)dx = \int_2^0 (2x+x^6)dx | \int_2^0 x(2+x^5)dx = \int_2^0 (2x+x^6)dx &= -\int_0^2 (2x+x^6)dx | ||
= \left(\frac{2x^2}{1+1}+\frac{x^6+1}{6+1}\right)\bigg|_{0}^{2}=\left(x^2+\frac{x^7}{7}\right)\bigg|_{0}^{2} | = \left(\frac{2x^2}{1+1}+\frac{x^6+1}{6+1}\right)\bigg|_{0}^{2}=\left(x^2+\frac{x^7}{7}\right)\bigg|_{0}^{2} | ||
= \left((2)^2+\frac{(2)^7}{7}\right)-\left((0)^2+\frac{0^7}{7}\right) | = \left((2)^2+\frac{(2)^7}{7}\right)-\left((0)^2+\frac{0^7}{7}\right) | ||
Revision as of 21:03, 6 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{2}^{0}x(2+x^{5})dx=\int _{2}^{0}(2x+x^{6})dx&=-\int _{0}^{2}(2x+x^{6})dx=\left({\frac {2x^{2}}{1+1}}+{\frac {x^{6}+1}{6+1}}\right){\bigg |}_{0}^{2}=\left(x^{2}+{\frac {x^{7}}{7}}\right){\bigg |}_{0}^{2}=\left((2)^{2}+{\frac {(2)^{7}}{7}}\right)-\left((0)^{2}+{\frac {0^{7}}{7}}\right)=4+{\frac {2^{7}}{7}}={\frac {156}{7}}\end{aligned}}}