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人気のある微分積分 >

integral from 0 to 1 of 5xsqrt(2x+9)

解

\int_{0}^{1} 5 x 2 x + 9 d x

解

81 - 2211

+1

十進法表記

8.03425 \dots

解答ステップ

\int_{0}^{1} 5 x 2 x + 9 d x

定数を除く:

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

= 5 \cdot \int_{0}^{1} x 2 x + 9 d x

u置換積分法を適用する

= 5 \cdot \int_{9}^{11} \frac{u ( u - 9 )}{4} d u

定数を除く:

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

= 5 \cdot \frac{1}{4} \cdot \int_{9}^{11} u (u - 9) d u

拡張

u (u - 9) : u^{\frac{3}{2}} - 9 u

= 5 \cdot \frac{1}{4} \cdot \int_{9}^{11} u^{\frac{3}{2}} - 9 u d u

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

= 5 \cdot \frac{1}{4} (\int_{9}^{11} u^{\frac{3}{2}} d u - \int_{9}^{11} 9 u d u)

\int_{9}^{11} u^{\frac{3}{2}} d u = \frac{242 11 - 486}{5}

\int_{9}^{11} 9 u d u = 9 (\frac{22 11}{3} - 18)

= 5 \cdot \frac{1}{4} (\frac{242 11 - 486}{5} - 9 (\frac{22 11}{3} - 18))

簡素化

5 \cdot \frac{1}{4} (\frac{242 11 - 486}{5} - 9 (\frac{22 11}{3} - 18)) : 81 - 2211

= 81 - 2211

グラフ

人気の例

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

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\int_{0}^{3} k x d x

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

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

integral from 1 to e of 8xln(x)

\int_{1}^{e} 8 x ln (x) d x