5.4 Indefinite Integrals and the Net Change Theorem/39: Difference between revisions
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<math>\int_{1}^{64}\frac{1}{x^{1/2}}</math> + <math>\int_{1}^{64}\frac{x^{1/3}}{x^{1/2}}</math> | <math>\int_{1}^{64}\frac{1}{x^{1/2}}</math> + <math>\int_{1}^{64}\frac{x^{1/3}}{x^{1/2}}</math> | ||
<math>\int_{1}^{64}x^{-1/2}+x^{1/3-1/2}</math> = <math>\int_{1}^{64}x^{-1/2}+x^{-1/6}</math> | = <math>\int_{1}^{64}x^{-1/2}+x^{1/3-1/2}</math> = <math>\int_{1}^{64}x^{-1/2}+x^{-1/6}</math> | ||
Add one to the exponents and divide by the new exponent | Add one to the exponents and divide by the new exponent | ||
<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(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> | ||
<math>16+38.4 - (2+1.2)</math> | = <math>16+38.4 - (2+1.2)</math> | ||
<math>54.4 - 3.2</math> | = <math>54.4 - 3.2</math> | ||
<math>51.2 = \frac{256}{5}</math> | = <math>51.2 = \frac{256}{5}</math> | ||
Revision as of 10:05, 29 August 2022
![{\displaystyle \int _{1}^{64}{\frac {1+{\sqrt[{3}]{x}}}{\sqrt {x}}}dx}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/cdb02981593f318bab17caae838949d55b200cb6)
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