integral from 0 to 2 of integral from x to 2 of 2y^2sin(xy)

Lösung

\int_{0}^{2} \int_{x}^{2} 2 y^{2} sin (x y) d y d x

- sin (4) + 4

Dezimale

4.75680 \dots

Schritte zur Lösung

\int_{0}^{2} \int_{x}^{2} 2 y^{2} sin (x y) d y d x

Reihenfolge der Integration ändern

= \int_{0}^{2} \int_{0}^{y} 2 y^{2} sin (x y) d x d y

\int_{0}^{y} 2 y^{2} sin (x y) d x = 2 y (- cos (y^{2}) + 1)

= \int_{0}^{2} 2 y (- cos (y^{2}) + 1) d y

\int_{0}^{2} 2 y (- cos (y^{2}) + 1) d y = - sin (4) + 4

= - sin (4) + 4

\int \int x y d x d y

\int \int (x^{2} + y^{2}) d x d y

\int \int \int 1

\int_{0}^{π} \int_{0}^{π} cos (x + y) d x d y

\int_{π}^{2 π} \int_{0}^{π} (sin (x) + cos (y)) d x d y