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-7 to 1 of xsqrt(2-x)

解

\int_{- 7}^{1} x 2 - x d x

解

- \frac{932}{15}

+1

十進法表記

- 62.13333 \dots

解答ステップ

\int_{- 7}^{1} x 2 - x d x

u置換積分法を適用する

= \int_{9}^{1} - (- u + 2) u d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{9} - (- u + 2) u d u

定数を除く:

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

= - (- \int_{1}^{9} (- u + 2) u d u)

拡張

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

= - (- \int_{1}^{9} - u^{\frac{3}{2}} + 2 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

= - (- (- \int_{1}^{9} u^{\frac{3}{2}} d u + \int_{1}^{9} 2 u d u))

\int_{1}^{9} u^{\frac{3}{2}} d u = \frac{484}{5}

\int_{1}^{9} 2 u d u = \frac{104}{3}

= - (- (- \frac{484}{5} + \frac{104}{3}))

簡素化

- (- (- \frac{484}{5} + \frac{104}{3})) : - \frac{932}{15}

= - \frac{932}{15}

グラフ

人気の例

integral from-1 to 2 of [(x^2)-(x+2)]

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

integral from 0 to 28 of sqrt(1+9/4 x)

\int_{0}^{28} 1 + \frac{9}{4} x d x

integral from 2 to 5 of sqrt(x/(x+1))

\int_{2}^{5} \frac{x}{x + 1} d x

integral from 3 to 5 of (x-3)^4(5-x)^2

\int_{3}^{5} (x - 3)^{4} (5 - x)^{2} d x

integral from-0.1 to 0.9 of-1600x

\int_{- 0.1}^{0.9} - 1600 x d x