5.4 Indefinite Integrals and the Net Change Theorem/39: Difference between revisions

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= <math>\int_{1}^{64}\frac{x^{1/2}}{\frac{1}{2}}+ \frac{x^{5/6}}{\frac{5}{6}}</math> = <math>\int_{1}^{64}2x^\frac{1}{2} + \frac{6}{5}x^\frac{5}{6}</math>
= <math>\int_{1}^{64}\frac{x^{1/2}}{\frac{1}{2}}+ \frac{x^{5/6}}{\frac{5}{6}}</math> = <math>\int_{1}^{64}2x^\frac{1}{2} + \frac{6}{5}x^\frac{5}{6}</math>


=<math>2(x)^\frac{1}{2} + \frac{6}{5}(x)^\frac{5}{6}\bigg|_{-2}^{2}</math>
=<math>2(x)^\frac{1}{2} + \frac{6}{5}(x)^\frac{5}{6}\bigg|_{64}^{1}</math>


= <math>2(64)^\frac{1}{2} + \frac{6}{5}(64)^\frac{5}{6} - (2(1)^\frac{1}{2} + \frac{6}{5}(1)^\frac{5}{6})</math>
= <math>2(64)^\frac{1}{2} + \frac{6}{5}(64)^\frac{5}{6} - (2(1)^\frac{1}{2} + \frac{6}{5}(1)^\frac{5}{6})</math>

Revision as of 10:24, 29 August 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 \int_{1}^{64}\frac{1+\sqrt[3]{x}}\sqrt{x}dx}

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 \int_{1}^{64}\frac{1}{x^{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 \int_{1}^{64}\frac{x^{1/3}}{x^{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 \int_{1}^{64}x^{-1/2}+x^{1/3-1/2}} = 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 \int_{1}^{64}x^{-1/2}+x^{-1/6}}

Add one to the exponents and divide by the new exponent

= 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 \int_{1}^{64}\frac{x^{1/2}}{\frac{1}{2}}+ \frac{x^{5/6}}{\frac{5}{6}}} = 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 \int_{1}^{64}2x^\frac{1}{2} + \frac{6}{5}x^\frac{5}{6}}

=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|_{64}^{1}}

= 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(64)^\frac{1}{2} + \frac{6}{5}(64)^\frac{5}{6} - (2(1)^\frac{1}{2} + \frac{6}{5}(1)^\frac{5}{6})}

= 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}}

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