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 2pi(x+9)x^2

解

\int_{0}^{1} 2 π (x + 9) x^{2} d x

解

\frac{13 π}{2}

+1

十進法表記

20.42035 \dots

解答ステップ

\int_{0}^{1} 2 π (x + 9) x^{2} d x

定数を除く:

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

= 2 π \cdot \int_{0}^{1} (x + 9) x^{2} d x

拡張

(x + 9) x^{2} : x^{3} + 9 x^{2}

= 2 π \cdot \int_{0}^{1} x^{3} + 9 x^{2} 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

= 2 π (\int_{0}^{1} x^{3} d x + \int_{0}^{1} 9 x^{2} d x)

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} 9 x^{2} d x = 3

= 2 π (\frac{1}{4} + 3)

簡素化

2 π (\frac{1}{4} + 3) : \frac{13 π}{2}

= \frac{13 π}{2}

グラフ

人気の例

(1+y)dx-(1-x)dy=0

(1 + y) d x - (1 - x) d y = 0

limit as x approaches 10 of x/2

x \to 10 lim (\frac{x}{2})

derivative y=e^{7x+1}

d er i v a t i v e y = e^{7 x + 1}

integral of x^2*(1+2x^3)^5

\int x^{2} \cdot (1 + 2 x^{3})^{5} d x

derivative of 9sqrt(x)-1/x

\frac{d}{d x} (9 x - \frac{1}{x})