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 3 of (3x-2)(x+3)

解

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

解

\frac{45}{2}

+1

十進法表記

22.5

解答ステップ

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

3 x - 2

の共役で乗じる

\frac{9 x ^{2} - 4}{3 x + 2}

= \int_{- 2}^{3} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x

未定義の (特異) 点を求める:

x = - \frac{2}{3}

存在する場合は

b, a < b < c, f (b) =

未定義

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 2}^{- \frac{2}{3}} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x + \int_{- \frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x

\int_{- 2}^{- \frac{2}{3}} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x = - \frac{344}{27}

\int_{- \frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x = \frac{1903}{54}

= - \frac{344}{27} + \frac{1903}{54}

簡素化

- \frac{344}{27} + \frac{1903}{54} : \frac{45}{2}

= \frac{45}{2}

グラフ

人気の例

integral from 0 to 1 of sqrt(x)+x^2

\int_{0}^{1} x + x^{2} d x

integral from-1 to 1 of e^xx

\int_{- 1}^{1} e^{x} x d x

integral from-1 to 1 of x(x+4)^2

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

integral from 0 to pi/2 of sec(x)tan(x)

\int_{0}^{\frac{π}{2}} sec (x) tan (x) d x

integral from 1 to 4 of ln(2x)

\int_{1}^{4} ln (2 x) d x