# Calculate the iterated integral int_0^2 int_0^3e^(x-y)dy dx

Calculate the iterated integral ${\int }_{0}^{2}{\int }_{0}^{3}{e}^{x-y}dydx$
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i4epdp
${\int }_{0}^{2}{\int }_{0}^{3}{e}^{x-y}dydx$
$={\int }_{0}^{2}\left[-{e}^{x-y}{\right]}_{0}^{y=3}dx$
$=-{\int }_{0}^{2}\left(-{e}^{x-3}-{e}^{x}\right)dx$
$=-\left[{e}^{x-3}-{e}^{x}{\right]}_{0}^{2}$
$=-\left[\left({e}^{-1}-{e}^{2}\right)-\left({e}^{-3}-{e}^{0}\right)\right]$
$={e}^{2}-\frac{1}{e}+\frac{1}{{e}^{3}}-1$