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人気のある微分積分 >

integral from-3 to 1 of (2x+1)(3+x)(1-x)

解

\int_{- 3}^{1} (2 x + 1) (3 + x) (1 - x) d x

解

- \frac{32}{3}

+1

十進法表記

- 10.66666 \dots

解答ステップ

\int_{- 3}^{1} (2 x + 1) (3 + x) (1 - x) d x

2 x + 1

の共役で乗じる

\frac{4 x ^{2} - 1}{2 x - 1}

= \int_{- 3}^{1} \frac{4 x ^{2} - 1}{2 x - 1} (3 + x) (1 - x) d x

未定義の (特異) 点を求める:

x = \frac{1}{2}

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_{- 3}^{\frac{1}{2}} \frac{4 x ^{2} - 1}{2 x - 1} (3 + x) (1 - x) d x + \int_{\frac{1}{2}}^{1} \frac{4 x ^{2} - 1}{2 x - 1} (3 + x) (1 - x) d x

\int_{- 3}^{\frac{1}{2}} \frac{4 x ^{2} - 1}{2 x - 1} (3 + x) (1 - x) d x = - \frac{1127}{96}

\int_{\frac{1}{2}}^{1} \frac{4 x ^{2} - 1}{2 x - 1} (3 + x) (1 - x) d x = \frac{103}{96}

= - \frac{1127}{96} + \frac{103}{96}

簡素化

- \frac{1127}{96} + \frac{103}{96} : - \frac{32}{3}

= - \frac{32}{3}

グラフ

人気の例

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