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人気のある微分積分 >

integral from 0 to x of 1/2 x

解

\int_{0}^{x} \frac{1}{2} x d x

解

\frac{x ^{2}}{4}

解答ステップ

\int_{0}^{x} \frac{1}{2} x d x

定数を除く:

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

= \frac{1}{2} \cdot \int_{0}^{x} x d x

べき乗則を適用する

= \frac{1}{2} [\frac{x ^{2}}{2}]_{0}^{x}

限度を計算する:

\frac{x ^{2}}{2}

= \frac{1}{2} \cdot \frac{x ^{2}}{2}

簡素化

= \frac{x ^{2}}{4}

人気の例

integral from 3 to 9 of 1/x

\int_{3}^{9} \frac{1}{x} d x

integral from 0 to ln(2) of (e^{2x})

\int_{0}^{l n (2)} (e^{2 x}) d x

integral from 0 to 2 of sin(npix)

\int_{0}^{2} sin (nπ x) d x

integral from 0 to 14 of (10e^x)

\int_{0}^{14} (10 e^{x}) d x

integral from-pi/4 to pi/4 of cos^2(2x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} cos^{2} (2 x) d x