integral from 1 to 2 of (v^3+5v^6)/(v^2)

解

\int_{1}^{2} \frac{v ^{3} + 5 v ^{6}}{v ^{2}} d v

\frac{65}{2}

十進法表記

32.5

解答ステップ

\int_{1}^{2} \frac{v ^{3} + 5 v ^{6}}{v ^{2}} d v

拡張

\frac{v ^{3} + 5 v ^{6}}{v ^{2}} : \frac{v ^{3}}{v ^{2}} + \frac{5 v ^{6}}{v ^{2}}

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{v ^{3}}{v ^{2}} d v + \int_{1}^{2} \frac{5 v ^{6}}{v ^{2}} d v

\int_{1}^{2} \frac{v ^{3}}{v ^{2}} d v = \frac{3}{2}

\int_{1}^{2} \frac{5 v ^{6}}{v ^{2}} d v = 31

= \frac{3}{2} + 31

簡素化

\frac{3}{2} + 31 : \frac{65}{2}

= \frac{65}{2}