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人気のある微分積分 >

integral from 1 to k of k/(2w^2)

解

\int_{1}^{k} \frac{k}{2 w ^{2}} d w

解

\frac{- 1 + k}{2}

解答ステップ

\int_{1}^{k} \frac{k}{2 w ^{2}} d w

定数を除く:

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

= \frac{k}{2} \cdot \int_{1}^{k} \frac{1}{w ^{2}} d w

べき乗則を適用する

= \frac{k}{2} [- \frac{1}{w}]_{1}^{k}

限度を計算する:

- \frac{1}{k} + 1

= \frac{k}{2} (- \frac{1}{k} + 1)

簡素化

= \frac{- 1 + k}{2}

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integral from 1 to 3 of x^2e^{-x}

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