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人気のある微分積分 >

integral from 0 to 3 of (3x+2)(x-5)

解

\int_{0}^{3} (3 x + 2) (x - 5) d x

解

- \frac{123}{2}

+1

十進法表記

- 61.5

解答ステップ

\int_{0}^{3} (3 x + 2) (x - 5) d x

3 x + 2

の共役で乗じる

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

= \int_{0}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) 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_{0}^{\frac{2}{3}} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) d x + \int_{\frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) d x

\int_{0}^{\frac{2}{3}} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) d x = - \frac{250}{27}

\int_{\frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) d x = - \frac{2821}{54}

= - \frac{250}{27} - \frac{2821}{54}

簡素化

- \frac{250}{27} - \frac{2821}{54} : - \frac{123}{2}

= - \frac{123}{2}

グラフ

人気の例

integral from 0 to 27 of sqrt(3x)

\int_{0}^{27} 3 x d x

integral from pi/2 to 2pi of sin(x)

\int_{\frac{π}{2}}^{2 π} sin (x) d x

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\int_{0}^{4} x - x^{2} d x

integral from 50 to 100 of x/(14+3x^2)

\int_{50}^{100} \frac{x}{14 + 3 x ^{2}} d x

integral from 2 to 4 of 2x+3

\int_{2}^{4} 2 x + 3 d x