integral from 0 to 4 of integral from sqrt(x) to 2 of sin(y^3)

解

\int_{0}^{4} \int_{x}^{2} sin (y^{3}) d y d x

\frac{1}{3} (- cos (8) + 1)

十進法表記

0.38183 \dots

解答ステップ

\int_{0}^{4} \int_{x}^{2} sin (y^{3}) d y d x

積分の順序を変更する

= \int_{0}^{2} \int_{0}^{y^{2}} sin (y^{3}) d x d y

\int_{0}^{y^{2}} sin (y^{3}) d x = y^{2} sin (y^{3})

= \int_{0}^{2} y^{2} sin (y^{3}) d y

\int_{0}^{2} y^{2} sin (y^{3}) d y = \frac{1}{3} (- cos (8) + 1)

= \frac{1}{3} (- cos (8) + 1)