integral from 0 to 1 of (3x+1)cos(x)

解

\int_{0}^{1} (3 x + 1) cos (x) d x

4 sin (1) + 3 cos (1) - 3

十進法表記

1.98679 \dots

解答ステップ

\int_{0}^{1} (3 x + 1) cos (x) d x

部分積分を適用する

= [(3 x + 1) sin (x) - \int 3 sin (x) d x]_{0}^{1}

\int 3 sin (x) d x = - 3 cos (x)

= [(3 x + 1) sin (x) - (- 3 cos (x))]_{0}^{1}

簡素化

= [sin (x) (3 x + 1) + 3 cos (x)]_{0}^{1}

限度を計算する:

4 sin (1) + 3 cos (1) - 3

= 4 sin (1) + 3 cos (1) - 3