Wiskunde Multiple Choice Vraag

$\int_{-2}^{+2}e^{\|x\|}\,dx=$	A. 0
B. e² − 2
C. 2e² − 1
D. 2e² − 2
E. \(\large \boldsymbol{\frac{1\,-\,e^4}{e^2}}\)

1^ste manier :
De functie $f(x)=e^{|x|}$ is even zodat
$\int_{-2}^{+2}e^{|x|}\,dx=2\int_{0}^{+2}e^x\,dx=2\left[e^x \right]_0^2=2(e^2-e^0)=2e^2-2$
2^de manier :
$\inline\\\int_{-2}^{+2}e^{|x|}\,dx=\int_{-2}^{0}e^{-x}\,dx+\int_{0}^{2}e^{|x|}\,dx\\=-\int_{-2}^{0}e^{-x}\,d(-x)+\int_{0}^{2}e^x\,dx\\=-\left[e^{-x}\right]_{-2}^0+\left[e^x \right]_0^2=-(e^0-e^2)+e^2-e^0\\=-1+e^2+e^2-1=2e^2-2$