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i have some difficulty to finish this integral, can you show me how to find the result of this integration?

$$\int(1/2)e^{-|x|} dx $$ for (-$m$ to $m$) whdere $m$ is a real number.

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    $\begingroup$ Write it as a sum of two integrals. One from $-m$ to $0$, the other from $0$ to $m$. $\endgroup$ – GEdgar Feb 5 '14 at 18:53
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Hint: This is an even function, so $$\int_{-m}^m\frac{1}{2}e^{|x|}dx=\int_{0}^me^{|x|}dx=\int_{0}^me^{x}dx$$

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  • $\begingroup$ True, but I think my hint is more instructive. $\endgroup$ – GEdgar Feb 5 '14 at 22:07
  • $\begingroup$ @user42388 how it work? can u explain it to me? $\endgroup$ – valerie Feb 6 '14 at 0:07
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    $\begingroup$ Suppose $f(x)$ is an even function. Then $\int_{-m}^mf(x)dx=\int_{-m}^0f(x)dx+\int_{0}^mf(x)dx$ Now make a change of variables to the first integral $x->-x$. So you get $\int_{o}^mf(x)dx+\int_{0}^mf(x)dx=2\int_0^mf(x)dx$ $\endgroup$ – user42388 Feb 6 '14 at 0:25

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