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人気のある微分積分 >

integral from 0 to 2 of 2xsqrt(12-x^2)

解

\int_{0}^{2} 2 x 12 - x^{2} d x

解

163 - \frac{32 2}{3}

+1

十進法表記

12.62786 \dots

解答ステップ

\int_{0}^{2} 2 x 12 - x^{2} d x

定数を除く:

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

= 2 \cdot \int_{0}^{2} x 12 - x^{2} d x

u置換積分法を適用する

= 2 \cdot \int_{12}^{8} - \frac{u}{2} d u

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

= 2 (- \int_{8}^{12} - \frac{u}{2} d u)

定数を除く:

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

= 2 (- (- \frac{1}{2} \cdot \int_{8}^{12} u d u))

べき乗則を適用する

= 2 (- (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{8}^{12}))

簡素化

2 (- (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{8}^{12})) : [\frac{2}{3} u^{\frac{3}{2}}]_{8}^{12}

= [\frac{2}{3} u^{\frac{3}{2}}]_{8}^{12}

限度を計算する:

163 - \frac{32 2}{3}

= 163 - \frac{32 2}{3}

グラフ

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