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

Damien Horton 2022-07-27 Answered

Calculate the iterated integral

\int_{0}^{2} \int_{0}^{3} e^{x - y} d y d x

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i4epdp

Answered 2022-07-28 Author has 12 answers

\int_{0}^{2} \int_{0}^{3} e^{x - y} d y d x

= \int_{0}^{2} [- e^{x - y}]_{0}^{y = 3} d x

= - \int_{0}^{2} (- e^{x - 3} - e^{x}) d x

= - [e^{x - 3} - e^{x}]_{0}^{2}

= - [(e^{- 1} - e^{2}) - (e^{- 3} - e^{0})]

= e^{2} - \frac{1}{e} + \frac{1}{e^{3}} - 1

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