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

Lösung

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

1 - \frac{1}{e}

Dezimale

0.63212 \dots

Schritte zur Lösung

\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}

\int_{1}^{2} \int_{- v}^{v} e^{\frac{u}{v}} \cdot \frac{1}{2} d u d v

\int \int x d x d x

\int \int - 2 d x d y

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

\int \int \frac{6}{7} x^{\frac{6}{7}} d x d x