integral from 1 to 3 of (y^4+1/(4y^4))

解

\int_{1}^{3} (y^{4} + \frac{1}{4 y ^{4}}) d y

\frac{39269}{810}

十進法表記

48.48024 \dots

解答ステップ

\int_{1}^{3} y^{4} + \frac{1}{4 y ^{4}} d y

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} y^{4} d y + \int_{1}^{3} \frac{1}{4 y ^{4}} d y

\int_{1}^{3} y^{4} d y = \frac{242}{5}

\int_{1}^{3} \frac{1}{4 y ^{4}} d y = \frac{13}{162}

= \frac{242}{5} + \frac{13}{162}

簡素化

\frac{242}{5} + \frac{13}{162} : \frac{39269}{810}

= \frac{39269}{810}