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人気のある微分積分 >

integral from-2 to 0 of x^2sqrt(1-x^3)

解

\int_{- 2}^{0} x^{2} 1 - x^{3} d x

解

\frac{52}{9}

+1

十進法表記

5.77777 \dots

解答ステップ

\int_{- 2}^{0} x^{2} 1 - x^{3} d x

u置換積分法を適用する

= \int_{9}^{1} - \frac{u}{3} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{9} - \frac{u}{3} d u

定数を除く:

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

= - (- \frac{1}{3} \cdot \int_{1}^{9} u d u)

べき乗則を適用する

= - (- \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9})

簡素化

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

限度を計算する:

\frac{52}{3}

= \frac{1}{3} \cdot \frac{52}{3}

簡素化

= \frac{52}{9}

グラフ

人気の例

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\int_{0}^{a r c t a n (x)} sec^{2} (t) d t

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\int_{0}^{1} x^{3} - 3 x^{2} + 2 d x

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integral from 1 to 9 of sqrt((11)/x)

\int_{1}^{9} \frac{11}{x} d x