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人気のある微分積分 >

integral from 6 to 9 of 2400xsqrt(3+2x)

解

\int_{6}^{9} 2400 x 3 + 2 x d x

解

8064021 - 3600015

+1

十進法表記

230111.50357 \dots

解答ステップ

\int_{6}^{9} 2400 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

= 2400 \cdot \int_{6}^{9} x 3 + 2 x d x

u置換積分法を適用する

= 2400 \cdot \int_{15}^{21} \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

= 2400 \cdot \frac{1}{4} \cdot \int_{15}^{21} u (u - 3) d u

拡張

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

= 2400 \cdot \frac{1}{4} \cdot \int_{15}^{21} 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

= 2400 \cdot \frac{1}{4} (\int_{15}^{21} u^{\frac{3}{2}} d u - \int_{15}^{21} 3 u d u)

\int_{15}^{21} u^{\frac{3}{2}} d u = \frac{882 21}{5} - 9015

\int_{15}^{21} 3 u d u = 3 (1421 - 1015)

= 2400 \cdot \frac{1}{4} (\frac{882 21}{5} - 9015 - 3 (1421 - 1015))

簡素化

2400 \cdot \frac{1}{4} (\frac{882 21}{5} - 9015 - 3 (1421 - 1015)) : 8064021 - 3600015

= 8064021 - 3600015

グラフ

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