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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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