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Popular >

integral from 0 to 2 of integral from 2x to 4 of e^{-x-2y}

Solution

\int_{0}^{2} \int_{2 x}^{4} e^{- x - 2 y} d y d x

Solution

\frac{e ^{10} - 5 e ^{2} + 4}{10 e ^{10}}

+1

Decimal Notation

0.09985 \dots

Solution steps

\int_{0}^{2} \int_{2 x}^{4} e^{- x - 2 y} d y d x

Change order of integration

= \int_{0}^{4} \int_{0}^{\frac{y}{2}} e^{- x - 2 y} d x d y

\int_{0}^{\frac{y}{2}} e^{- x - 2 y} d x = - e^{- \frac{y}{2} - 2 y} + e^{- 2 y}

= \int_{0}^{4} (- e^{- \frac{y}{2} - 2 y} + e^{- 2 y}) d y

\int_{0}^{4} (- e^{- \frac{y}{2} - 2 y} + e^{- 2 y}) d y = \frac{e ^{10} - 5 e ^{2} + 4}{10 e ^{10}}

= \frac{e ^{10} - 5 e ^{2} + 4}{10 e ^{10}}

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of integral from 2x to 4 of e^{-x-2y} ?
The integral from 0 to 2 of integral from 2x to 4 of e^{-x-2y} is (e^{10}-5e^2+4)/(10e^{10)}