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人気のある微分積分 >

integral from-2 to 1 of (-5-2x^2)^2

解

\int_{- 2}^{1} (- 5 - 2 x^{2})^{2} d x

解

\frac{807}{5}

+1

十進法表記

161.4

解答ステップ

\int_{- 2}^{1} (- 5 - 2 x^{2})^{2} d x

因数

- 5 - 2 x^{2} : - (5 + 2 x^{2})

= \int_{- 2}^{1} (- (5 + 2 x^{2}))^{2} d x

簡素化

(- (5 + 2 x^{2}))^{2} : (5 + 2 x^{2})^{2}

= \int_{- 2}^{1} (5 + 2 x^{2})^{2} d x

拡張

(5 + 2 x^{2})^{2} : 25 + 20 x^{2} + 4 x^{4}

= \int_{- 2}^{1} 25 + 20 x^{2} + 4 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

= \int_{- 2}^{1} 25 d x + \int_{- 2}^{1} 20 x^{2} d x + \int_{- 2}^{1} 4 x^{4} d x

\int_{- 2}^{1} 25 d x = 75

\int_{- 2}^{1} 20 x^{2} d x = 60

\int_{- 2}^{1} 4 x^{4} d x = \frac{132}{5}

= 75 + 60 + \frac{132}{5}

簡素化

75 + 60 + \frac{132}{5} : \frac{807}{5}

= \frac{807}{5}

グラフ

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