integral from 1 to 3 of (4x-3)^2-(x^2)^2

解

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

\frac{184}{15}

十進法表記

12.26666 \dots

解答ステップ

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

\int_{1}^{3} (4 x - 3)^{2} d x = \frac{182}{3}

\int_{1}^{3} (x^{2})^{2} d x = \frac{242}{5}

= \frac{182}{3} - \frac{242}{5}

簡素化

\frac{182}{3} - \frac{242}{5} : \frac{184}{15}

= \frac{184}{15}