integral from 0 to pi/4 of x*sin(x)

解

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

\frac{1}{2} - \frac{π}{4 2}

十進法表記

0.15174 \dots

解答ステップ

\int_{0}^{\frac{π}{4}} x sin (x) d x

部分積分を適用する

= [- x cos (x) - \int - cos (x) d x]_{0}^{\frac{π}{4}}

\int - cos (x) d x = - sin (x)

= [- x cos (x) - (- sin (x))]_{0}^{\frac{π}{4}}

簡素化

= [- x cos (x) + sin (x)]_{0}^{\frac{π}{4}}

限度を計算する:

\frac{1}{2} - \frac{π}{4 2}

= \frac{1}{2} - \frac{π}{4 2}