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

The integral from-2 to-1 of (4x^3+2/(y^3)) is 2/(y^3)-15

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

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

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

Solution steps

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

Apply the Sum Rule:

\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

\int_{0}^{x} e^{- y} d y

\int_{- \frac{3}{2}}^{\frac{3}{2}} x^{3} - x + 2 d x

\int_{- 2}^{2} x (x^{2} - 9) d x

\int_{0}^{2} (x^{3} + 4 x) d x

\int_{0}^{2} 2 4 - x^{2} d x

What is the integral from-2 to-1 of (4x^3+2/(y^3)) ?
The integral from-2 to-1 of (4x^3+2/(y^3)) is 2/(y^3)-15