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 0 to 1 of 5x^4(6-x^5)

解

\int_{0}^{1} 5 x^{4} (6 - x^{5}) d x

解

\frac{11}{2}

+1

十進法表記

5.5

解答ステップ

\int_{0}^{1} 5 x^{4} (6 - x^{5}) 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^{4} (6 - x^{5}) d x

拡張

x^{4} (6 - x^{5}) : 6 x^{4} - x^{9}

= 5 \cdot \int_{0}^{1} 6 x^{4} - x^{9} d x

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 (\int_{0}^{1} 6 x^{4} d x - \int_{0}^{1} x^{9} d x)

\int_{0}^{1} 6 x^{4} d x = \frac{6}{5}

\int_{0}^{1} x^{9} d x = \frac{1}{10}

= 5 (\frac{6}{5} - \frac{1}{10})

簡素化

5 (\frac{6}{5} - \frac{1}{10}) : \frac{11}{2}

= \frac{11}{2}

グラフ

人気の例

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

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

integral from 1 to 2 of 1/x+x

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

integral from 0 to pi/2 of (1+cos(2x))/2

\int_{0}^{\frac{π}{2}} \frac{1 + cos ( 2 x )}{2} d x

integral from 0 to 1 of (x^3)/(1000)

\int_{0}^{1} \frac{x ^{3}}{1000} d x

integral from 1 to 7 of (x+1)

\int_{1}^{7} (x + 1) d x