integral from 1 to 8 of 3x^2+1/(12x^2)

解

\int_{1}^{8} 3 x^{2} + \frac{1}{12 x ^{2}} d x

\frac{49063}{96}

十進法表記

511.07291 \dots

解答ステップ

\int_{1}^{8} 3 x^{2} + \frac{1}{12 x ^{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}^{8} 3 x^{2} d x + \int_{1}^{8} \frac{1}{12 x ^{2}} d x

\int_{1}^{8} 3 x^{2} d x = 511

\int_{1}^{8} \frac{1}{12 x ^{2}} d x = \frac{7}{96}

= 511 + \frac{7}{96}

簡素化

511 + \frac{7}{96} : \frac{49063}{96}

= \frac{49063}{96}