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Thursday, 18 August 2011

Math GRE - #18

If we have \[F(x)=\int_e^x{\log{t}dt}\] for all positive $x$, then $F'(x)=$

  • $x$
  • $\frac{1}{x}$
  • $\log{x}$
  • $x\log{x}$
  • $x\log{x}-1$

Solution :

I decided to use this question because of it's similarity to the question I posted yesterday. Since the derivative of an integral is itself (FTC - Part I), we have \[F'(x)=\frac{d}{dx}\int_e^x{\log{t}dt}=\log{x}.\]


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