integral from-1 to 1 of (x^3-(3x)/5)^2

解

\int_{- 1}^{1} (x^{3} - \frac{3 x}{5})^{2} d x

\frac{8}{175}

十進法表記

0.04571 \dots

解答ステップ

\int_{- 1}^{1} (x^{3} - \frac{3 x}{5})^{2} d x

拡張

(x^{3} - \frac{3 x}{5})^{2} : x^{6} - \frac{6 x ^{4}}{5} + \frac{9 x ^{2}}{25}

= \int_{- 1}^{1} x^{6} - \frac{6 x ^{4}}{5} + \frac{9 x ^{2}}{25} 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_{- 1}^{1} x^{6} d x - \int_{- 1}^{1} \frac{6 x ^{4}}{5} d x + \int_{- 1}^{1} \frac{9 x ^{2}}{25} d x

\int_{- 1}^{1} x^{6} d x = \frac{2}{7}

\int_{- 1}^{1} \frac{6 x ^{4}}{5} d x = \frac{12}{25}

\int_{- 1}^{1} \frac{9 x ^{2}}{25} d x = \frac{6}{25}

= \frac{2}{7} - \frac{12}{25} + \frac{6}{25}

簡素化

\frac{2}{7} - \frac{12}{25} + \frac{6}{25} : \frac{8}{175}

= \frac{8}{175}