5.3 The Fundamental Theorem of Calculus/28: Difference between revisions
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\int_{0}^{1}\left(3+x\sqrt{x}\right)dx &= \int_{0}^{1}\left(3+x^{1}{x}^{\frac{1}{2}}\right)dx | \int_{0}^{1}\left(3+x\sqrt{x}\right)dx &= \int_{0}^{1}\left(3+x^{1}{x}^{\frac{1}{2}}\right)dx | ||
= \int_{0}^{1}\left(3+x^{1+\frac{1}{2}}\right)dx = \int_{0}^{1}\left(3+x^{\frac{3}{2}}\right)dx \\ | = \int_{0}^{1}\left(3+x^{1+\frac{1}{2}}\right)dx = \int_{0}^{1}\left(3+x^{\frac{3}{2}}\right)dx \\ | ||
&= 3x+\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1} = +\frac{x^{\frac{5}{2}}}{\frac{5}{2}} | &= 3x+\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1} = 3x+\frac{x^{\frac{5}{2}}}{\frac{5}{2}} | ||
\end{align} | \end{align} | ||
Revision as of 21:38, 23 August 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{0}^{1}\left(3+x{\sqrt {x}}\right)dx&=\int _{0}^{1}\left(3+x^{1}{x}^{\frac {1}{2}}\right)dx=\int _{0}^{1}\left(3+x^{1+{\frac {1}{2}}}\right)dx=\int _{0}^{1}\left(3+x^{\frac {3}{2}}\right)dx\\&=3x+{\frac {x^{{\frac {3}{2}}+1}}{{\frac {3}{2}}+1}}=3x+{\frac {x^{\frac {5}{2}}}{\frac {5}{2}}}\end{aligned}}}