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人気のある微分積分 >

integral from-3 to 9 of-xcos(x)

解

\int_{- 3}^{9} - x cos (x) d x

解

- 9 sin (9) - cos (9) + 3 sin (3) + cos (3)

+1

十進法表記

- 3.36456 \dots

解答ステップ

\int_{- 3}^{9} - x cos (x) d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{- 3}^{9} x cos (x) d x

部分積分を適用する

= - [x sin (x) - \int sin (x) d x]_{- 3}^{9}

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

= - [x sin (x) - (- cos (x))]_{- 3}^{9}

簡素化

= - [x sin (x) + cos (x)]_{- 3}^{9}

限度を計算する:

9 sin (9) + cos (9) - 3 sin (3) - cos (3)

= - (9 sin (9) + cos (9) - 3 sin (3) - cos (3))

簡素化

= - 9 sin (9) - cos (9) + 3 sin (3) + cos (3)

グラフ

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