What is the integral from 1 to 4 of integral from 1 to sqrt(x of)2ye^{-x} ?

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integral from 1 to 4 of integral from 1 to sqrt(x of)2ye^{-x}

\int_{1}^{4} \int_{1}^{x} 2 y e^{- x} d y d x

- \frac{4}{e ^{4}} + \frac{1}{e}

Decimal Notation

0.29461 \dots

Solution steps

\int_{1}^{4} \int_{1}^{x} 2 y e^{- x} d y d x

\int_{1}^{x} 2 y e^{- x} d y = e^{- x} (x - 1)

= \int_{1}^{4} e^{- x} (x - 1) d x

\int_{1}^{4} e^{- x} (x - 1) d x = - \frac{4}{e ^{4}} + \frac{1}{e}

= - \frac{4}{e ^{4}} + \frac{1}{e}

\int x (x^{2} + 3)^{12} d x

\frac{\partial}{\partial y} (x^{2} - 3 x y)

30 y^{^{''}} - 25 y^{^{'}} = 0

\int x e^{x} d x

\int_{0}^{1} \frac{e ^{z} + 1}{e ^{z} + z} d z

What is the integral from 1 to 4 of integral from 1 to sqrt(x of)2ye^{-x} ?
The integral from 1 to 4 of integral from 1 to sqrt(x of)2ye^{-x} is -4/(e^4)+1/e