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人気のある微分積分 >

integral from 2 to 7 of 700xsqrt(3+2x)

解

\int_{2}^{7} 700 x 3 + 2 x d x

解

1428017 - 9807

+1

十進法表記

56285.11204 \dots

解答ステップ

\int_{2}^{7} 700 x 3 + 2 x d x

定数を除く:

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

= 700 \cdot \int_{2}^{7} x 3 + 2 x d x

u置換積分法を適用する

= 700 \cdot \int_{7}^{17} \frac{u ( u - 3 )}{4} d u

定数を除く:

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

= 700 \cdot \frac{1}{4} \cdot \int_{7}^{17} u (u - 3) d u

拡張

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

= 700 \cdot \frac{1}{4} \cdot \int_{7}^{17} u^{\frac{3}{2}} - 3 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

= 700 \cdot \frac{1}{4} (\int_{7}^{17} u^{\frac{3}{2}} d u - \int_{7}^{17} 3 u d u)

\int_{7}^{17} u^{\frac{3}{2}} d u = \frac{578 17 - 98 7}{5}

\int_{7}^{17} 3 u d u = 3417 - 147

= 700 \cdot \frac{1}{4} (\frac{578 17 - 98 7}{5} - (3417 - 147))

簡素化

700 \cdot \frac{1}{4} (\frac{578 17 - 98 7}{5} - (3417 - 147)) : 1428017 - 9807

= 1428017 - 9807

グラフ

人気の例

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

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

integral from 3 to 1 of 1

\int_{3}^{1} 1

integral from 0 to 4 of (11-x)sqrt(x)

\int_{0}^{4} (11 - x) x d x

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

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

integral from 0 to 2 of sqrt(1+2x)

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