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

解

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

- \frac{π}{16}

十進法表記

- 0.19634 \dots

解答ステップ

\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}