integral from 1 to 2 of (x^2+1/(4x^2))

解

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

\frac{59}{24}

十進法表記

2.45833 \dots

解答ステップ

\int_{1}^{2} x^{2} + \frac{1}{4 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}^{2} x^{2} d x + \int_{1}^{2} \frac{1}{4 x ^{2}} d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} \frac{1}{4 x ^{2}} d x = \frac{1}{8}

= \frac{7}{3} + \frac{1}{8}

簡素化

\frac{7}{3} + \frac{1}{8} : \frac{59}{24}

= \frac{59}{24}