integral from 0 to 4 of sqrt(y)cos(y)

解

\int_{0}^{4} y cos (y) d y

2 sin (4) - \frac{π}{2} § (4 \frac{2}{π}) + \frac{π}{2} § (0 \cdot \frac{2}{π})

解答ステップ

\int_{0}^{4} y cos (y) d y

部分積分を適用する

= [y sin (y) - \int \frac{sin ( y )}{2 y} d y]_{0}^{4}

\int \frac{sin ( y )}{2 y} d y = \frac{π}{2} § (\frac{2}{π} y)

= [y sin (y) - \frac{π}{2} § (\frac{2}{π} y)]_{0}^{4}

限度を計算する:

2 sin (4) - \frac{π}{2} § (4 \frac{2}{π}) + \frac{π}{2} § (0 \cdot \frac{2}{π})

= 2 sin (4) - \frac{π}{2} § (4 \frac{2}{π}) + \frac{π}{2} § (0 \cdot \frac{2}{π})