Question

Resolva o seguinte integral duplo:

Answer 1

Olá, Marlenguiliche.

$\int_0^1\int_x^{2x}e^{x-y}\,dy\,dx=\\\\ =\int_0^1\left -e^{x-y}\right|_x^{2x}\,dx=\\\\ =-\int_0^1 (e^{x-2x}-e^{x-x})\,dx=\\\\ =-\int_0^1 (e^{-x}-1)\,dx=\\\\ =-(\left -e^{-x}\right|_0^1-\left x\right|_0^1)=\\\\ =e^{-1}-e^0+1-0=\\\\ =\boxed{\frac1 e}$