5.4 Indefinite Integrals and the Net Change Theorem/39: Difference between revisions
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= \int_{1}^{64}\left(x^{-1/2}+x^{\frac{1}{3}-{\frac{1}{2}}}\right)dx = \int_{1}^{64}\left(x^{-\frac{1}{2}}+x^{-\frac{1}{6}}\right)dx \\[2ex] | = \int_{1}^{64}\left(x^{-1/2}+x^{\frac{1}{3}-{\frac{1}{2}}}\right)dx = \int_{1}^{64}\left(x^{-\frac{1}{2}}+x^{-\frac{1}{6}}\right)dx \\[2ex] | ||
&= \frac{x^{\frac{1}{2}}}{\frac{1}{2}}+ \frac{x^{\frac{5}{6}}}{\frac{5}{6}} = 2x^\frac{1}{2} + \frac{6}{5}x^\frac{5}{6} | &= \left[\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+ \frac{x^{\frac{5}{6}}}{\frac{5}{6}}\right]_{1}^{64} = 2x^\frac{1}{2} + \frac{6}{5}x^\frac{5}{6} | ||
Revision as of 16:20, 21 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_{1}^{64}\frac{1+\sqrt[3]{x}}\sqrt{x}dx &= \int_{1}^{64}\left(\frac{1}{x^{1/2}} + \frac{x^{1/3}}{x^{1/2}}\right)dx = \int_{1}^{64}\left(x^{-1/2}+x^{\frac{1}{3}-{\frac{1}{2}}}\right)dx = \int_{1}^{64}\left(x^{-\frac{1}{2}}+x^{-\frac{1}{6}}\right)dx \\[2ex] &= \left[\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+ \frac{x^{\frac{5}{6}}}{\frac{5}{6}}\right]_{1}^{64} = 2x^\frac{1}{2} + \frac{6}{5}x^\frac{5}{6} \end{align} }
=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 2(x)^\frac{1}{2} + \frac{6}{5}(x)^\frac{5}{6}\bigg|_{1}^{64}} =
= 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 16+38.4 - (2+1.2)}
= 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 54.4 - 3.2} = 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 51.2}
= 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 \frac{256}{5}}