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人気のある微分積分 >

integral from y to 1 of 3x

解

\int_{y}^{1} 3 x d x

解

\frac{3 ( 1 - y ^{2} )}{2}

解答ステップ

\int_{y}^{1} 3 x d x

定数を除く:

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

= 3 \cdot \int_{y}^{1} x d x

べき乗則を適用する

= 3 [\frac{x ^{2}}{2}]_{y}^{1}

限度を計算する:

\frac{1}{2} - \frac{y ^{2}}{2}

= 3 (\frac{1}{2} - \frac{y ^{2}}{2})

簡素化

= \frac{3 ( 1 - y ^{2} )}{2}

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