5.4 Indefinite Integrals and the Net Change Theorem/31: Difference between revisions
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\int_{0}^{1}x\left(\sqrt[3]{x}+\sqrt[4]{x}\right)dx &=\int_{0}^{1}x\left(x^{\frac{1}{3}}+x^{\frac{1}{4}}\right)dx=\int_{0}^{1}\left(x^{\frac{4}{3}}+x^{\frac{5}{4}}\right)dx \\[2ex] | \int_{0}^{1}x\left(\sqrt[3]{x}+\sqrt[4]{x}\right)dx &=\int_{0}^{1}x\left(x^{\frac{1}{3}}+x^{\frac{1}{4}}\right)dx=\int_{0}^{1}\left(x^{\frac{4}{3}}+x^{\frac{5}{4}}\right)dx \\[2ex] | ||
&= \left(\frac{3x^{\frac{7}{3}}{7}+\frac{4x^{\frac{9}{4}}{9}\right)\bigg|_{0}^{1} \\[2ex] | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 18:48, 22 September 2022
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int_{0}^{1}x\left(\sqrt[3]{x}+\sqrt[4]{x}\right)dx &=\int_{0}^{1}x\left(x^{\frac{1}{3}}+x^{\frac{1}{4}}\right)dx=\int_{0}^{1}\left(x^{\frac{4}{3}}+x^{\frac{5}{4}}\right)dx \\[2ex] &= \left(\frac{3x^{\frac{7}{3}}{7}+\frac{4x^{\frac{9}{4}}{9}\right)\bigg|_{0}^{1} \\[2ex] \end{align} }