5.3 The Fundamental Theorem of Calculus/35: Difference between revisions
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\int_{1}^{9}\frac{1}{2x}dx = \frac{1}{2}\int_{1}^{9}\frac{1}{x}dx | \int_{1}^{9}\frac{1}{2x}dx = \frac{1}{2}\int_{1}^{9}\frac{1}{x}dx | ||
&= \frac{1}{2}\ln{|x|}\bigg|_{1}^{9} = \frac{1}{2}\ln{|9|}-\frac{1}{2}\ln{|1|} | &= \frac{1}{2}\ln{|x|}\bigg|_{1}^{9} = \frac{1}{2}\ln{|9|}-\frac{1}{2}\ln{|1|} | ||
&= \ln{|9|} | &= \ln{|9|} | ||
Revision as of 19:27, 25 August 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{1}^{9}{\frac {1}{2x}}dx={\frac {1}{2}}\int _{1}^{9}{\frac {1}{x}}dx&={\frac {1}{2}}\ln {|x|}{\bigg |}_{1}^{9}={\frac {1}{2}}\ln {|9|}-{\frac {1}{2}}\ln {|1|}&=\ln {|9|}\end{aligned}}}