ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral from 2 to 4 of (2x^2)/(x+2)

解

\int_{2}^{4} \frac{2 x ^{2}}{x + 2} d x

解

2 (4 ln (\frac{3}{2}) + 2)

+1

十進法表記

7.24372 \dots

解答ステップ

\int_{2}^{4} \frac{2 x ^{2}}{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_{2}^{4} \frac{x ^{2}}{x + 2} d x

u置換積分法を適用する

= 2 \cdot \int_{4}^{6} \frac{( u - 2 ) ^{2}}{u} d u

拡張

\frac{( u - 2 ) ^{2}}{u} : u - 4 + \frac{4}{u}

= 2 \cdot \int_{4}^{6} u - 4 + \frac{4}{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

= 2 (\int_{4}^{6} u d u - \int_{4}^{6} 4 d u + \int_{4}^{6} \frac{4}{u} d u)

\int_{4}^{6} u d u = 10

\int_{4}^{6} 4 d u = 8

\int_{4}^{6} \frac{4}{u} d u = 4 ln (\frac{3}{2})

= 2 (10 - 8 + 4 ln (\frac{3}{2}))

簡素化

= 2 (4 ln (\frac{3}{2}) + 2)

グラフ

人気の例

integral from 7 to 13 of 4x^5

\int_{7}^{13} 4 x^{5} d x

integral from-1 to 9 of 0.048x^3-2x

\int_{- 1}^{9} 0.048 x^{3} - 2 x d x

integral from 1 to 5 of (5^{ln(x)})/x

\int_{1}^{5} \frac{5 ^{l n (x)}}{x} d x

integral from 2 to 4 of sqrt(4x-x^2)

\int_{2}^{4} 4 x - x^{2} d x

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

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