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-1 to 0 of pi(1-x^2)^2

解

\int_{- 1}^{0} π (1 - x^{2})^{2} d x

解

π \frac{8}{15}

+1

十進法表記

1.67551 \dots

解答ステップ

\int_{- 1}^{0} π (1 - x^{2})^{2} d x

定数を除く:

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

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

拡張

(1 - x^{2})^{2} : 1 - 2 x^{2} + x^{4}

= π \cdot \int_{- 1}^{0} 1 - 2 x^{2} + x^{4} 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

= π (\int_{- 1}^{0} 1 d x - \int_{- 1}^{0} 2 x^{2} d x + \int_{- 1}^{0} x^{4} d x)

\int_{- 1}^{0} 1 d x = 1

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

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

= π (1 - \frac{2}{3} + \frac{1}{5})

結合

1 - \frac{2}{3} + \frac{1}{5} : \frac{8}{15}

= π \frac{8}{15}

グラフ

人気の例

tangent f(x)=2x^3-x^2+3,(2,15)

t an g e n t f (x) = 2 x^{3} - x^{2} + 3, (2, 15)

sum from n=1 to infinity of (x^n)/(n!)

n = 1 \sum \infty \frac{x ^{n}}{n !}

integral of (30)/(1-cos(5x))

\int \frac{30}{1 - cos ( 5 x )} d x

integral of (x^6)/(sqrt(x^{14)-1)}

\int \frac{x ^{6}}{x ^{14} - 1} d x

(15y^2-xy)dx+x^2dy=0

(15 y^{2} - x y) d x + x^{2} d y = 0