Mathematics

The value of $\displaystyle \int _ { 0 } ^ { 10 } e ^ { \operatorname { sgn } ( x - [ x ] ) } d x$ equals (where $\left[.\right]$ represents the greatest integer function)

$10 e$

SOLUTION
$\displaystyle \int_0^{10} e^{sgn(x-[x])}dx$
$= \displaystyle \int_0^{10} e^{sgn\{x\}}dx$             $sgn(x) = \left\{\begin{matrix}1, & x > 0 \\ 0,& x=0\\ -1, &x<0 \end{matrix}\right.$
$=\displaystyle \int_0^{10}e'dx$       $(\because \{x\} > 0)$
$=ex|_0^{10}$
$= 10e$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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