integral from 1 to 2 of (y+5y^7)/(y^3)

解

\int_{1}^{2} \frac{y + 5 y ^{7}}{y ^{3}} d y

\frac{63}{2}

十進法表記

31.5

解答ステップ

\int_{1}^{2} \frac{y + 5 y ^{7}}{y ^{3}} d y

拡張

\frac{y + 5 y ^{7}}{y ^{3}} : \frac{1}{y ^{2}} + 5 y^{4}

= \int_{1}^{2} \frac{1}{y ^{2}} + 5 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}^{2} \frac{1}{y ^{2}} d y + \int_{1}^{2} 5 y^{4} d y

\int_{1}^{2} \frac{1}{y ^{2}} d y = \frac{1}{2}

\int_{1}^{2} 5 y^{4} d y = 31

= \frac{1}{2} + 31

簡素化

\frac{1}{2} + 31 : \frac{63}{2}

= \frac{63}{2}