What is the integral from 0 to 1 of integral from 0 to pi/2 of e^{-y}cos(x) ?

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integral from 0 to 1 of integral from 0 to pi/2 of e^{-y}cos(x)

\int_{0}^{1} \int_{0}^{\frac{π}{2}} e^{- y} cos (x) d x d y

1 - \frac{1}{e}

Decimal Notation

0.63212 \dots

Solution steps

\int_{0}^{1} \int_{0}^{\frac{π}{2}} e^{- y} cos (x) d x d y

\int_{0}^{\frac{π}{2}} e^{- y} cos (x) d x = e^{- y}

= \int_{0}^{1} e^{- y} d y

\int_{0}^{1} e^{- y} d y = 1 - \frac{1}{e}

= 1 - \frac{1}{e}

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\int \int - 2 d x d y

\int_{0}^{5} \int_{0}^{6} uv (1) d v d u

What is the integral from 0 to 1 of integral from 0 to pi/2 of e^{-y}cos(x) ?
The integral from 0 to 1 of integral from 0 to pi/2 of e^{-y}cos(x) is 1-1/e