What is the integral from 0 to pi/2 of integral from 0 to 2 of x^2ycos(xy^2) ?

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integral from 0 to pi/2 of integral from 0 to 2 of x^2ycos(xy^2)

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

- \frac{π}{16}

Decimal Notation

- 0.19634 \dots

Solution steps

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

\int_{0}^{2} x^{2} y cos (x y^{2}) d y = \frac{x sin ( 4 x )}{2}

= \int_{0}^{\frac{π}{2}} (\frac{x sin ( 4 x )}{2}) d x

\int_{0}^{\frac{π}{2}} (\frac{x sin ( 4 x )}{2}) d x = - \frac{π}{16}

= - \frac{π}{16}

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What is the integral from 0 to pi/2 of integral from 0 to 2 of x^2ycos(xy^2) ?
The integral from 0 to pi/2 of integral from 0 to 2 of x^2ycos(xy^2) is -pi/(16)