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人気のある微分積分 >

integral from 0 to a of (a^2x-x^3)

解

\int_{0}^{a} (a^{2} x - x^{3}) d x

解

\frac{a ^{4}}{2} - \frac{a ^{4}}{4}

解答ステップ

\int_{0}^{a} a^{2} x - x^{3} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{a} a^{2} x d x - \int_{0}^{a} x^{3} d x

\int_{0}^{a} a^{2} x d x = \frac{a ^{4}}{2}

\int_{0}^{a} x^{3} d x = \frac{a ^{4}}{4}

= \frac{a ^{4}}{2} - \frac{a ^{4}}{4}

人気の例

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