What is the integral from 0 to 2 of integral from x to 2 of 2y^2sin(xy) ?

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

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

- sin (4) + 4

Decimal

4.75680 \dots

Solution steps

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

Change order of integration

= \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

What is the integral from 0 to 2 of integral from x to 2 of 2y^2sin(xy) ?
The integral from 0 to 2 of integral from x to 2 of 2y^2sin(xy) is -sin(4)+4