integral from-2 to-1 of (4x^3+2/(y^3))

解

\int_{- 2}^{- 1} (4 x^{3} + \frac{2}{y ^{3}}) d x

\frac{2}{y ^{3}} - 15

解答ステップ

\int_{- 2}^{- 1} 4 x^{3} + \frac{2}{y ^{3}} 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_{- 2}^{- 1} \frac{2}{y ^{3}} d x + \int_{- 2}^{- 1} 4 x^{3} d x

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

\int_{- 2}^{- 1} 4 x^{3} d x = - 15

= \frac{2}{y ^{3}} - 15